Either

start W Raptors > wolves > gromp > blue > krugs/red > red/krugs > optionally scuttle > raptors > wolves gromp > take dragon/rift you will be level 5 here so you are usually stronger than the enemy jungler who is usually level 4 here.

Alternative:

start e wolves > raptors > krugs > red > blue > gromp > optinally scuttle > wolves > raptors > krugs > contest krugs/dragon

often i do the second buff last so that i can ward the nearby bush to check for invades while i kill the second to last camp

Many people will say to start the top side camp first so u can be at dragon at lvl 5 when dragon spawns. However it's often overly contested so if you instead start on the bottom side you can usually get the dragon side scuttle then finish your second clear reset buy and be near dragon before anyone seriously considers taking it. Trying to sneak dragon at spawn usually gets you countered by competent opponents.

Small disclaimer I'm only low emerald so my knowledge in this area may not be perfect or even good. If anyone has any further tips please add them in the comments for my own improvement.

Laners have a few tactics they use to stay up in farm and xp. The first is freezing. If a laner is stronger they'll usually try to deny the opponent gold/xp by holding a large wave at their allied tower and forcing the weaker opponent to either fight and die or stay back and lose out. your way of fixing this is to just go up and help 2v1 and push the wave in if your ally is being frozen on, or if your ally is freezing and you gank don't clear their freeze unless they ping assist or they start hardshoving.

The second is the slow push into a 2 man dive. Often one side who may have started with a freeze will last hit minions until their allied wave becomes very massive then theyll push it into the enemy tower so that the weaker person has to deal with the huge wave. This leaves the stronger player open to either reset, hit the tower, proxy or the best option is to dive the weaker opponent with help from the jungler and the huge wave. So if you know your laner is ahead and freezing make sure you are in the area for the slow push into the crash to see if a 2 man dive is viable. If your laner is weaker and being crashed on also be closeby and maybe even show in lane if they are posturing for a dive. Try not to deny your weak laner their xp/gold though if the enemy just backs off for a reset. If a laner gets dove and loses a huge wave the game is basically over for them. It's notable that a slightly weaker laner can do this as well if the enemy mismanages the wave because a minion advantage in a 1v1 can be lethal.

The third is if you see one of your laners not in lane you can usually take over their lane and get better xp and farm from lane and go back to farm your jungle later and if both laners are in a different lane push the tower down as fast as you can shyvana clears towers pretty fast. This is fairly prominent in the midlane since many midlaners like to roam and if you're not in position to help with that roam you can instead hard shove the mid lane while the enemy midlaner matches the roam. This can get you a lot of plating and even first tower many times. Objectives are more important than kills in my opinion so going for a questionable roam vs taking guarunteed xp and maybe opening up the map by pushing down a tower is my go to. You need to be careful doing this because if both laners were just resetting and you go and push at a bad time you could end up taking xp but the opponent makes it back in time to catch some of the xp and now you've just set your allied laner behind in xp. Its mostly okay to take the xp if it would have otherwise crashed into the tower though, or alternatively you could hold the wave until your allied wave shows up and the 2 waves hitting your allied wave will sometimes cause the minions to die faster and deny the enemy xp while holding a huge xp wave for your ally.

The fourth is just recognizing when your laner needs to reset. If your laner has mismanaged their wave or didnt have the clear speed solo or has low health/resource, or just has a lot of gold to spend they may ping for an assist in that case help them shove in their wave so they dont int and throw their lane. If the enemy stays in lane while your ally resets then either hold the wave or clear the wave and go back to farming.

The 5th is understanding what showing on the map does in your enemies minds. If you show bot lane and baron is up they may try to quickly grab baron or vice versa with dragon. If theyre on baron and you can't contest then try to shove a lane especially midlane as far and as fast as you can. Sometimes the pressure on their base can throw them off and make them lose coordination and if you get 2 towers and an inhib to their baron its not a terrible trade, and if you can't get that at least they don't have a wave at your base to push with immediately after they baron.

The 6th is recognizing your lane thats most vulnerable to a gank. Then you have two good options, one be in the area to counter gank or two go deeper into enemy/neutral territory and put a control ward to provide an early warning to that ally. You should also have a rough idea of where your enemy jungler is or most likely is and ping his location fairly often throughout the game to keep your allies aware.

The 7th is recognizing your winning lanes, farming lanes, losing lanes, and win conditions. This mostly takes experience to know which matchups are favorable for you. In general you want to gank lanes that are either a win condition for your team or who are already winning lanes. You don't want to gank farm lanes or losing lanes often since they can't back you up as well. A win condition can be something like a malphite/malzahar who has a gamechanging ultimate and good cc to guaruntee a kill if they get a little help, or a farm lane that gets a lead (ex: kog'maw lulu who gets ahead), or a snowbally lane that falls off late like a jayce/zed or it could be a yasuo/yone who if they dont get ahead will feed and if they get ahead will 1v9.

Shyvana's role varies based on her build. In general when you're ahead look for objectives. When you're behind group and look for picks.

If you play a build with 3 or more AP items then your role is backline in teamfights. You stay out of the thick of the fighting and lob dragonform E's and try to focus groups of enemies > highest threat squishy. If your team dies just live and use dragonform to clear waves from distance but most importantly survive. If you don't have dragonform you should farm safely until it's up. Having your ultimate when you need it is the most important macro for this build.

If you play a bruiser variant with 2 or more defensives you are a midline champion. This means you still don't want to be the primary engage but you do want to be the secondary. You want to peel off anyone who dives onto your carries and fight front to back.

If you play a tank variant then your job is to absorb damage and set the stage for a teamfight. If you're the only tank then wait for the enemy to misposition while your team is in position to follow up then engage on them. Mispositioning would be their squishies being in front, them having a numbers disadvantage, or clumping in a tight group. If their engage dives first then you have 2 options. Counter engage and dive into 3+ of them to drag them out of the fight then you do as much damage as you can until you die. Alternatively peel their dive and try to kite out the fight which is better when the enemies are spaced out and respecting you more.

If you play an AD variant your job in general is to avoid teamfights and instead split push and take as much pressure as possible off of your team. If split pushing isnt viable because your team is being pushed in start with ranged dragonform and do as much safe damage as you can from safety to soften them up and hope they dont have an enchanter to counter all of your damage. If you're in human form fight front to back. If you have dragonform available and your team has engage, wait for your team to start the engage then dive the enemy back line from an angle and delete them before they delete you. If you don't have any engage on your team and its all squishy carries including you then look for picks and avoid being focused since you usually have the highest single target and aoe dps on your team. Fighting front to back in human form then transitioning into diving their backline with your dragonform can sometimes be best since it gives you time to stack terminus and pta from relative safety. You have a ton of mixed percent health damage between your E mark and Botrk so tanks die to you as easily as squishies do anyways.

Q is an auto attack reset.

During early ganks don't lead with e while in human form, walk up to them and auto see how they react then throw ur e into an auto q auto. The less distance there is between you and the enemy the less likely you are to miss. The opposite is true in dragon form.

Between auto attacks make sure you orb walk with them, shyvanas weakness is being kited. However this tip is less applicable for AP Shyvana.

There is a setting in game to change your left click to attack move and another setting to make it attack move on cursor this helps significantly with orb walking/kiting. Consider turning off movement with the map if you use this.

If you often get tilted there is a check box which will remove allied chat and/or all chat in the in game settings. /mute all is another temporary option you can use if you just dont want to listen for that one game.

Survival and maintaining a high pace are the cornerstones of a successful shyvana.

Win Condition will often be dragon soul for shyvana. Each dragon shyvana takes is 120 gold worth of free stats for her due to her passive.

Giving up the first dragon to secure an experience/jungling pace lead is a viable strategy despite most people always talking about how she can do early dragons. Most enemy junglers know this and will constantly keep vision to try to prevent this anyways and if you get caught it resets your momentum.

If you're being counter jungled place a redward in the bushes at your jugle entrance and consider switching to yellow trinket as well. Yellow/blue trinket is more valuable when you're behind and red trinket is more valuable when you're ahead.

Think about yourself as a ball rolling down a hill steadly gaining momentum. This is you when you are jungling as shyvana. Every time you die you lose significant amounts of that momentum but the longer you're alive the harder that ball is going to hit when it lands.

Levels through gaining experience are more valuable than items gained through gold. Soak experience but don't take punishment for gold.

Proper use of R is dependent on build, if you are squishy use R as either an escape or just use it out of the fight to spam E into the enemy. It's rarely good to try to R+E on a squishy build for a 1 shot because of the difficulty with the hitbox at close range. R into someone/group and then E can be good but its very risky and not highly recommended. Also with the cast time required to actually get E on the ground if you were jumping into a large group its more likely you could get off more damage in the same time just by spamming Q since with modest cdr it instantly resets then following up with E on any who get away. The haste to instantly reset when hitting 5 targets is between 70 and 75. 100 haste to instantly reset on 4 targets. Instant resets will net you 1500-2500 dps per target on any build.

Trinity + dragonforce build notes:

This is the build I came up with to give shyvana reasonable human form capability while still maintaining a reasonable team fight aoe ranged damage. Detailed below I'll do my best to explain why by showing some of the potential of items by themselves (so if you bought them as your first item this is what you'd get roughly speaking). This is just to get a basic understanding of what these items are kind of doing for shyvana without factoring in synergies these items have with other items. However I do consider synergies to the best of my ability when coming up with the complete build, but I needed to choose my build based off of the most synergetic 1 item spike.

DPS against a default target dummy for the first item slot tested for 5k total damage on the dummy and got the average dps using every cooldown as fast as possible at level 6. one combo burst = ewaq and walk out to not keep using e burn. dragonform e is the full damage if they stood in the burn the entire time. Character has 3 points e everything else 1 point. Used the conquerer rune page for this test. There is some human error in the tests.

Shojin -
one combo burst - 697
one combo burst (prestacked shojin) - 732
sustained damage base form - 294
sustained damage dragonform - 358
dragonform e - 625 - 702 n cd: 7.41

Trinity -
one combo burst - 823
sustained damage base form - 340
sustained damage dragonform - 381
dragonform e - 597 cd: 8.33

titanic -
one combo burst - 1045
sustained damage base form - 284
sustained damage dragonform - 334
titanic passive to secondarys - 86 (this would go up a lot with more health)
dragonform e - 603 cd: 10

nashors -
one combo burst - 771
sustained damage base form - 290
sustained damage dragonform - 364
dragonform e - 743 cd: 8.7

botrk -
one combo burst - 829
sustained damage base form - 296 (testing is a bit bad cuz dummy runs out of health)
sustained damage dragonform - 347
dragonform e - 608 cd: 10

Liandrys - (i dont count dps after i stopped hitting)
one combo burst - 754
sustained damage base form - 191
sustained damage dragonform - 247
dragonform e - 907 cd: 10

rabadons -
one combo burst - 826
sustained damage base form - 196
sustained damage dragonform - 262
dragonform e - 948 cd: 10

Based on these numbers I chose Trinity as the best first item for good sustained damage in dragonform and base form and good cooldown for reasonable damage on the E. I chose liandrys second because much of its damage is based on enemy health rather than your own AP and synergizes well with cdr from other items. I chose shojin third because it synergizes with spamming spellcasting which helps with more liandrys procs and consistency with the spellblade passive from trinity and shojin just synergizes perfectly with everything shyvana does. Sorc shoes are my default because they're as much magic pen as you'd get from cryptbloom until the enemy is 51 magic resist and before that they're just a better pen item. It helps more than ionians in my experience. The last two slots are more flexible I chose jak'sho and terminus because jak'sho passive stacks with the dragonborn passive and terminus passive for a decent armor and mr boost. Terminus I chose because it synergizes with jak sho its highly gold efficient and the penetration means no one in late game is safe from you. Terminus is also very fast to stack when hitting multiple targets in dragonform with the q. Rabadons and shadowflame/crypt/void would be much better damage if you mostly just want to cast e from range in late game and you could sell trinity for nashors at that point too for about 670 gold after full build for a bit better damage. Nashors isn't really better dps than trinity until you have a few hundred AP and even then trinity brings health and movement speed to the table as well. You could also do anti heal and a darkseal in the last 2 item slots its very flexible. Jak'sho and terminus are mostly just to cover your weaknesses rather than to add to your strengths. If you go jak'sho terminus then getting some form of sustain would help a lot which is why I run conquerer but if you're not going for sustain then pta is better for burst damage and fleet is better for surviving shorter trades. Conquerer is a lategame rune and feels much worse than pta early in my experience so it may be better to stick with pta I'm still testing, but my intial analysis for full build you're looking at around 3-4k health and 180-250 in resistances and conquerer could heal about 60-120 health per second per target you're hitting which is very good considering shyvana has both aoe damage and sustained damage and is durable enough to survive a while. Sorcery secondary tree is better if you're going the AP caster route, but I prefer the resolve tree to give a little more durability which when added with the dragonborn passive is considerable and can get you through the early to midgame without having to build much resistance.

I know most people choose either shojin or nashors first over trinity. The reason I choose trinity is because the first item spike make you a monster. Nashors normally doesn't feel good until you have rabadons and shojin is good on its own but its still worse than trinity by itself Shojin shines more in amplifying the damage from other items via its absurd haste and damage passive. With trinity a lot of your damage is in your spellblade passive it makes the human form not as useless as other items meaning you can fight while in base form then transform mid fight rather than feeling useless and having to farm until you have ult every time. Trinity spellblade is doing 156 damage vs nashors 35 on hit so you'd have to get about 5 hits with nashors to make up the gap in damage and while nashors has 17 percent more attack speed it also has 45 less ad and 300 less health, so why make yourself weaker on your first item buy and delay a portion of your powerspike. I prefer to rush my powerspikes and while nashors synergizes better with rabadons and shojin synergizes better with liandrys they both delay a portion of your powerspike and I'd prefer to gain momentum as early as possible. Blade of the ruined king is another option people go with first and while it is better late game trinity is better early game just because people have lower health pools and trinitys damage is loaded into burst and trinity synergizes better with liandrys and spellcasting in general because of its decent ability haste and botrk leaves you much more susceptible to being burst before you get your damage off than trinity does. Shojin is a very good item on shyvana but it doesn't excel as well at base form damage nor sustained clear speed and is more of a capstone item for shyvana to bring trinity and liandrys damage fully online. Shojin is an item that is good at any point but its main benefit is its synergy with shyvanas kit and any other item you could build so if you want more flexibility in your build based on the game then shojin could be a better first item, but again I'll choose trinity because if I don't have dragonform at least I still have a ton of damage and movespeed.

The downside of going trinity instead of the normal shojin or nashors build is that trinity doesn't have any synergy with E other than the 20 ability haste so you are forced to auto attack some to get off a good portion of your damage. The general consensus at this time (that I don't really agree with) is that late game you are forced to become an E bot on shyvana in order to get off reasonable damage because otherwise you get bursted, kited, or ccd too hard in team fights. Fundamentally I think this is flawed because you want to use shyvanas full kit including q autos and liandrys gives a good chunk of the ranged AP damage for the E which makes up some of the gap of not going full AP. Also if a lategame team fight starts and you either don't have ult or they kite out and wait your ult to run out before reengaging then you are useless as AP where as this mixed build is strong even in human form and can rapidly restack the dragonform. The build definitely isnt a 1v9 carry though late game because you did build mostly damage items so you're not tanky enough to survive everyone at the same time.

How to use this build:
farm until trinity force
after trinity force you win almost all 1v1s
if you get ahead go shojin second if your even or behind liandrys second
shojin lets you spam spellcasting where liandrys gives the teamfight/skirmishing damage from safety
4th and 5th item is game dependent if its all squishies go rabadons - shadowflame to burst them down if the main threat are bruisers go jak'sho terminus or terminus jak sho into tanks but dont be afraid to go kaenic, FoN, randuins, or any other situational item.

with trinity you don't need dragonform to fight the move speed passive means you can usually run people down or kite out 1v1s you might not win straight up so doing full burst combos and walking out while waiting on cds is a tactic. You have good objective control and great farming clear speed. Mix in differeent tactics of heavy farming, objective control, punishing enemys for over extending and counter jungling. You can do all of these well the hardest part is pre trinity force you are weaker than most for ganking. For teamfights do NOT dive solo let your engage go before you then you can follow up on their engage after they eat some of the cc and burst. If you have no engage on your team stay back and poke with fireballs with your team and kite them out fight front to back.

As for the second item slot, while many items like titanic botrk or rabadons would be higher damage, liandrys is by far the best ranged aoe damage and you do need to have some damage on your dragonform e especially in late team fights to soften the enemy before you fully commit. A greedier but probably better for skirmishes and 1v1 is to do shojin before liandrys but liandrys second is better if you need to stay out of the fight longer and spam E from range.

As a small sidenote I'm in emerald with this build and I managed to go from gold 1 to emerald 4 with an 79 percent win rate on an alt using the trinity build. With the shojin liandrys build I did this with a 64 percent win rate. I don't know if this is because I got better or because of changes in the game or otherwise. I just thought it was interesting antecdotal data.

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Shojin liandrys build:

Shojin liandrys pta and riftmaker all have a damage multiplier for the fight which stack multiplicatively (1.12*1.08*1.08*1.1 = 1.43x damage most of which amplifies liandrys burn damage as well. Other damage amplifiers like coup de grace and horizon focus would also amplify this further.

Shojin provides 35 percent cdr good health damage and it multiples ability damage by 12 percent. Do not build any thing else until shojin is complete not t1 boots not a dark seal not anything. The shojin power spike makes you too strong to delay it.

Liandrys is probably the best damage item shyvana can get because she applies it very easily especially in team fights. The nice thing is that every time one of shyvanas dots ticks it applies an extra tick of liandrys damage and refreshes the duration so every time your w ticks or the dragon form e aoe on the ground ticks. This stacks up a lot especially if youre in the middle of multiple people which the juggernaut build allows you to do often.

Sorc shoes are simply the best boots for shyvana. I've tried all of them and you just dont have enough damage in the midgame where you're strongest with any other boots.

Jak'sho gives resistances when you need it the most right after liandrys. Shojin liandrys and sorc shoes give all the damage you really need

Riftmaker adds more damage and potentially some sustain in fights.

Steraks gage benefits from all of the other items that gave hp and the shield gives time for you to regain health via riftmaker passive so in some situations it could nearly triple your durability (base life + steraks shield of 80 percent bonus health + all of the health restored during those 4.5 seconds of shield via riftmaker aoe healing).

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Botrk - joat notes:

Advantages: The build order allows for the best clear speed and gives quick 5 ability haste/10 adaptive from joat. 600 gold into your second item, you would have the full power of joat via mote and cloth armor. Botrk into iceborn has been a tried and true AD setup on shyvana through the years but warmogs or randuins may be a viable alternative to iceborn. Shojin lets you spam your q and e and get more spellblade procs off with iceborn and gives you greatly improved ranged dps for teamfights when you cant rush in. The early dark seal in a Bruiser build also has the unique synergy of you having more tanky stats and hence being less likely to die and lose the stacks as well as adding to the absurd stat check nature of shyvana.

Disadvantages: the rune shards have to be for scaling rather than the early clear which makes your first clear particularly vulnerable. However this quickly becomes irrelevant after your first back. just be careful of the early invades. Note that if you're doing a reverse clear you could just back after your first buff and get a dagger and heal before going to your last buff and camp. (reverse clear example: raptors - wolves - gromp - blue - back - krugs - red - raptors - wolves - gromp - dragon/gank with lvl 5 advantage). Another main disadvantage is that it relies on you staying alive and farming well so that you dont lose momentum but this is true in all shyvana builds.

Shyvana holds a unique trait of being able to build any and everything so why not fully utilize that capability by adapting to each stage of the game. Jack of all trades is great gold value early and is the best secondary rune set for midgame shyvana which is the peak of shyvanas strength (shes weak early and falls off late game as a general rule).

My problem with shyvana is that she's always had an identity crisis. She excels at attack speed, AP, has bruiser stats via her passive and ult and she has an auto attack reset for on hit builds. This means that over the years people have only utilized a particular fraction of her kit rather than the entire thing. This build allows for you to fully utilize every single one of shyvanas strengths.

Analysis of the jungle items and why i chose mosstomper:

Blue smite is great for clear speed, rotations and maintaining a high tempo which is critical for a farm dependent champion. Red is great in that it gives an extra slow that shyvana can utilize well. Specifically red synergizes with shyvana dragonform E when you have liandrys because the slow will keep them in the burn on the ground making them take extra damage from both the e burn and refreshing liandrys. However green smite is best when we build botrk, because we aren't building a health item first. Which means that percentage wise we are gaining a lot more. For instance if you built shojin - liandrys you would have 600 bonus health vs botrk - iceborn you only have 300 bonus health. if you built mosstomper on each that'd be a ~50 percent increase in bonus health for shojin - liandrys vs a 100 percent increase for botrk - iceborn (assuming mosstomper was a 300 hp shield albeit it scales to level but im just using as an example). tldr: Botrk first often leaves you too squishy and you need the extra health to get your damage off.

analysis of rune shards:
normally you would run attack speed - adaptive - health. This gives you a lot more early game capability in that it allows you to fight if you're invaded. However being invaded is mostly only relevant for the first clear and is the obvious weakest point of shyvanas game, so instead of running shards that are best for the first 5 minutes of the game i'd rather run runes that emphasize the strongest point of shyvanas games (midgame). the clear speed is only a few seconds slower on the first clear and almost neglible on all future clears. Furthermore with us building botrk first we are far squishier and our ability haste is really low as compared to shojin first item. Running haste and double scaling lets us make up for what we're not getting by not building shojin. Attack speed is relevant in getting your dragon form back however haste lets you q more anyways which is an attack speed steroid so the tradeoff isnt too terrible. Noteably if you're running this build during your first clear if you're doing blue - gromp first then taking q second would be better than w as you need the extra attack speed to proc the onhit from your e.

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Noteable items:

horizon focus - damage amp similar to rabadons in a lower ap build

liandrys - has a burn that shyvana applies frequently via her 0.5 second ticks on her w and dragonform e ground burn so it gets a deceptive amount of damage, since it scales off of enemy health the general consensus is its not synergetic with rabadons, it has a nice new component that helps with jungle clearing as well for only 900 gold so its just a really well rounded item and deceptively powerful item on shyvana

rabadons - possibly the best item on shyvana but the components are expensive and the high ap can be counterbalanced by other items passives or just the cheap nature of other items

cryptbloom vs voidstaff - these percent magic pen items are extremely efficient 3rd items, the general consensus is cryptbloom is better because the 15 ability haste and heal passive out weigh the higher percent pen of voidstaff

nashors tooth - good for clearing objectives quickly, stacking fury for more ults, and since q procs the on hit damage twice its stronger than something like lichbane; fantastic for taking towers

spear of shojin - often a first item on shyvana because it has 35 percent cdr on all of her abilities and a 12 percent ability damage amp which synergizes with things like liandrys and riftmaker both of which have damage amps that multiply together, when you combine this with pta and possibly horizon focus you could be doing up to 50 percent more damage per ability

oblivion orb/Morellonomicon - cheap anti heal that is easily applied to large groups by shyvana has great synergy with liandrys since liandrys extends the timer from 3 seconds to at least 6 seconds this is your go to anti heal

bramble vest/thornmail - a more niche anti heal when you really need armor like against darius

botrk - the changes to botrk give more base stats and better clear speed now plus the slow being on third hit is much better for shyvana, this item is a very powerful rush item but leaves you a bit squishy and moves a lot of your burst into your auto attacks and away from your ranged abilities

titanic hydra - excellent item if you build a lot of health in that it lets you fight front to back in team fights and still damage the squishies from far away, theres a unique synergy where say 3 people are in melee range of u and 2 squishies are behind them if you q in dragonform youll probably hit all 3 twice with the titanic and your auto then the 3 in front will send 6 of the passive damage hits to each of the two squishies in the back which can cause them to get absolutely deleted

sundered sky - double crit if you lead with q on the first hit and since in dragonform you can hit multiple people if you change targets each attack you could hit 10 crits per enemy player in a niche situation where all 5 were clumped together and you dragonform qd each enemy once it'd end up being 50 critical hits in 5 q casts, it'd never happen to that extent but the point is it can let you delete teams

warmogs - lets you stay on the map and rotate quicker has a huge amount of health that counters burst champions but falls to sustained damage champions

randuins - borderline necessary anti crit item atm with how broken crit is for any tanky/bruiser build, basically a crit would normally do at least 1.75x damage and randuins would multiply that by 0.7 taking 30 percent of the damage off taking the damage down to 1.225x this is most pronounced against infinity edge and sundered sky abusers

kaenic - the renewing magic shield makes burst mages almost neglible

frozen heart - deceptively powerful anti attack speed item that gains a lot of value in team fights because the down scaling of attack speed hurts on hit builds and such for example if an opponent has 2.0 attack speed it would become 1.6 attack speed instead negating 1200 gold worth of attack speed off of that one person alone, considering you can apply this to all 5 enemies in a team fight and that it has a range of 700 units (further than even caitlins attack range) its deceptively valuable, and it has another hidden ability in that it counts as being in combat when youre in range to activate it even if people are hidden in bushes so your liandrys riftmaker or jaksho passives would all stack up just by being in 700 units of enemy range

blackfire torch - decent on shyvana with high ap but is weaker than liandrys

riftmaker - mostly built for the synergy passives with liandrys and shojin in that their passives have multiplicative damage stacking you could even build a haunting guise afterwards for more damage multplying

abyssal mask - its more of a support item but can triple as a modestly tanky pen item as well it has decent synergy if you have 3 ap champions on your team including you

force of nature - this is an anti magic damage over time so its good against sunfire cape liandrys amumu stuff like that

jak sho - has reasonable synergy with shyvanas passive such that normally you'd have to build tank items to make it good to use for the synergy with passive but shyvana can get away with taking dragons and making it stronger

rylais - has deceptive synergy with syvanas dragonform E, the slow keeps them in the burn on the ground longer which means it effectively boosts your AP ratio on your dragonform E by probably 20-30 percent, but considering you have something like 210 AP ratio on that for base damage then only 90 percent over 4 seconds you're only boosting the abilities damage by maybe 10 percent, still its deceptively underrated and the sticking power with this item means it shouldn't be as slept on as it is, the reason its overlooked is shyvana doesnt have something like brands burn which keeps it applied for long periods of time and there are arguably better damage items for shyvana and the health on it doesnt really give enough tanky stats for a bruiser build

shadowflame - crit is good with burn builds, the flat pen is stronger the earlier you get it

storm surge - since this ability procs 2 seconds after you do your damage it can effectively extend burn builds an extra 2 seconds, its not the strongest item on its own and i wouldnt recommend getting it first item can be a reasonable boot replacement lategame.