Pros

Very fast clears
Naturally tanky
MANALESS!
A lot of damage output

Cons

No crowd control except a knock back from ultimate
Weak ganks

Greater Mark of Hybrid Penetration

Greater Seal of Armor

Greater Glyph of Magic Resist

Greater Glyph of Cooldown Reduction

Greater Quintessence of Movement Speed

So some people might ask, why not AD runes? Well, her Burnout AD ratio is horrid and it's only good for her Twin Bite but I still think that building AD on her is worthless.

Some early game magic resist but more over per level magic resist for late game as you don't need early game magic resist since only champions do magic damage.

There are 3 item builds that are all situational, I will explain each item build why and when to use them, but first we'll have to go through basics.

START
Basically the standard start that everyone does. Warding totem is best for early game and once you get to mid game switch to sweeping lens.
+
+ X5

EARLY GAME
Once you hit the Spirit of the Ancient Golem your clears become ridiculously fast, and your naturally given resistances so that mean's the health added to you will synergize real nice with your dragon form resistances, and since Shyvana has a lot of high damage output, she'll be a real threat if she sits on the enemy team as she can tank them and chip away at there health.
+
MID GAME
So right now mid game should look something like this, which will increase your team fight potential and will give your team a whole bunch of resists. You can just sit on the enemy team and do massive amounts of AoE damage while tanking all there hits. Your high damage output will show no mercy for the weak who try to penetrate your dragon skin.
+ OR +
NOTE: Do not get Locket of the Iron Solari if the enemy team is all AD, stay at Aegis of the Legion or build a Randuin's Omen first.

Also get Sweeping Lens as you are going to try to clear wards around objectives.

LATE GAME
Now your 6 item build is complete, once you get randuin's omen you lessen the enemy ADC's DPS if he focuses you, and of course it gives a lot more HP!. We just get Warmog's Armor as there's no point in stacking more armor since they already have Last Whisper so we'll just try and beat there DPS off with more HP. Also now with Randuin's Omen you have an AoE slow around you, so now you do have some crowd control!
+

Max W, then E, and then Q.

I max WBurnout first because of the fast campclear

Then i max E Flame Breath because it is nice because of the extreme dmg u can deal with it and it have a long range so its easy to ensure kills with it too

And last i max Q Twin Bite the reason i don´t max this 2nd is because Flame Breath scales better and the cooldown on Flame Breth reduces w/ points in the ability

Level 1 : Burnout - auto attacks.

Level 2 : Burnout - auto attacks - Twin Bite

Level 3 : Flame Breath - Burnout - auto attack - Twin Bite

I feel that Shyvana is one of the best junglers, who excels at clearing the jungle because of the high damage output and mobility from Burnout. With the increase % damage from Spirit Stone gives even faster clears.

Usually when I jungle Shyvana, I always have the mentality of farming hard and also going to where the enemy jungler might be, as Shyvana isn't the best ganker but damn once she goes in a fight where the enemy blew their gap closers / escapes, there's no turning back now for them and now its up to them to withstand the heavy farmed dragon. So I will have about 100 cs while the enemy may have a few kills and 50 CS. I only counter gank or gank very over extended lanes. I only gank rarely. I know that if I gank there's a slim chance I'll get a kill unless that I can already somehow get in melee range. Also, most of the time I'll want to have flash by my side, just so I can secure kills.

Always keep tabs on your blue buff/red buff and do them immediately or have some ward coverage so the enemy jungler doesn't steal it, he will steal your red buff (blue side) if you're ganking top and he notices you started there and it's 7:15 minutes. I may not counter jungle a whole lot but I do like to protect my own jungle.

Some Junglers out there will not keep tabs on their buff, and at 7:15 if you know he started blue on purple side and you see him ganking top, that's a free blue for you. Little notes like these will make you a better counter jungler and player.

Basically, a gank early game isn't easy to pull off. If you're already behind him, you just activate burnout and catch up to him, hit him with a Flame Breath and activating Burnout and do an auto attack + Twin Bite combo and just keep attacking him. The reason this is hard to do is because the only CC that Shyvana will bring early is red buff, a smart player will just either flash once you get in melee range of her when you're behind him or just CC you and walk away.

I don't like these ganks at all, I only like to gank when I hit level 6 as I have gained access to my gap closer and an extra nuke, with this kit I can actually deal damage and keep up with the enemy.

Once you get your ultimate, you basically start off a gank with Dragon's Descent unless of course already behind him, and activiting Burnout when your sort of in range of the enemy and the same Flame Breath + auto attack + Twin Bite combo and just keep hitting the enemy. If you are already behind him wait until he blows an escape and then Dragon's Descent.
A counter gank gives freedom for Shyvana to output her high damage onto the enemy longer and is easier since the enemy probably just blew all their **** on your ally.

Shyvana is a decent duelist, she has a double auto attack and a auto reset but the only thing is she'll need a red buff + burnout to chase down people and doesn't have a lockdown like most junglers.

Shyvana meets dragon, who wins the half dragon or the dragon? The half dragon.

Mid Game

Mid game you should have Spirit of the Ancient Golem and Aegis of the Legion, you shouldn't die instantly since you have bonus resists and you can easily get out of the frey with the bonus movement speed from Burnout.

Time for you to lead your team to push towers, maintain control over dragon/baron and win. So always have a Vision Ward on dragon. And if you feel real confident, do it on baron and try to secure it and estimate whether you should do baron or not (some of enemy team is around bot side, your grouped 5) etc.

Shyvana's pretty good at doing baron/dragon, as her Flame Breath gives 2% of maximum health on auto attacks (it actually caps at 100 max damage source: Riot Employee Source) So when you do a AA + Twin Bite combo it does 300 damage, it's still pretty good damage, add on to her dragon form which can tank a lot of damage coming from the baron / dragon.

This is where also the best team fights come alive, since everyone is around level 13 and multiple variables happen instead of late game where it's peel for carries.

You should have a Randuin's Omen at this time as the enemy ADC should have a The Bloodthirster/ Infinity Edge + Phantom Dancer and will do tons of damage. Attack Speed reduction will cut a ADC's DPS massively, although once he gets that Last Whisper, he'll still be doing tons of damage. Just remember when you're chunked to disengage/retreat to an ally and let them switch focus off you, though this part is kind of easy with shyvana as she has a lot of movement speed in team fights with her Burnout.

If you get super super late game, I think that Shyvana is one of the best late game characters as not only is she tanky, but her kit allows her to build damage, so you can replace one of your items with a Ravenous Hydra or a Blade of the Ruined King, and also you can replace your boots with Zephyr. Since she doesn't bring a lot of crowd control, you should build some damages and be like a good anti carry. Also late game damage > tank since armor penetration and life steal and what not.

Bot Lane is dead/back. Reason: When doing dragon, it would be a 4v2 if they try to contest it.

You see bot lane recall and your mid and bot lane help do dragon.

Mid laner down. Reason: Mid is basically worth 1.5x of an ADC early game, because of the level advantage.

So you have a clear advantage at dragon.

You feel confident on doing it. You feel that the enemy team won't contest, feeling more powerful, etc.

Can solo it with

Spirit of the Ancient Golem after level 7, with dragon form can do it a bit better and with Flame Breath can be brought down swiftly.

Can dragon form over the wall on blue side and kill dragon if you know the dragon isn't warded but around it is.

Vision warded, can solo or ask for some help.

Shyvana can tank the dragon easily with the free armor and do a lot of damage with her triple flame breath proc combo on it, and is easily do-able with 3-4 members.