Not Updated For Current Season
Udyr - Burst like a Beast.
First off, there are Many ways to play Udyr and still do well. You can go AP, you can go Tank, you can go Atk speed, whatever. This guide focuses on Burst damage with Tiger strike. I will explain how it works.
First off, you will not be using pheonix stance at all, except to farms creep waves late game. Simply isn't the best damage you can do, tiger stance in small fights, or even team fights, is better.
How you say? Well lets go into some details. Udyr's tiger stance activation at rank 5 does three times his attack damage over two seconds, while doing his normal attacks still. Since we are going to abuse this fact we dont need attack speed much at all. You will still have 100%+ without any items in tiger stance while twisting your stance due to your passive. Then when you figure in Phantom Dancers 45% atk speed, you're golden, more then u need.
So lets go into a few things before we hit up items. Masteries, i went 21-9-0 for nimbleness. Its handy while jungling, as well as ur passive gives u 9% dodge while twisting your stances. If you're up against a team with little to no crowd control (stuns, roots, etc) get ninja tabi for serious dodge, and nimbleness procs. If you're up against a CC heavy team. You can choose to alter your spec to 21-0-9 for more experience, and get merc treads. Play it by ear.
I choose Heal and Ghost since Heal i find more useful then smite. Smite is only useful on level 1 to kill golem, past that, i find it quite a waste. Heal isnt amazing either, but can occasionally save your life or the life of a teammate, while still helping alot when jungling. Ghost is for when u need to get the hell out of dodge, and they pop ghost on u to catch you, or tables turned, they pop ghost to get out when ur chasing. Bear stance is nice when they dont ghost out, or in on u, but bear stance isnt always enough, just doesnt last long enough.
Marks - Armor Pen, so you hit harder, simple enough
Seals - I choose HP/level seals since they are broader, can be used against anybody, and synergize well with atmas impaler. Dodge seals are viable as well, if u want to go nimbleness, and ninja tabi against a physical auto atk style team.
Glyphs - I went magic res/level since he already get 4 armor per level base, and with atmas, armor isnt an issue. To balance out his defense a bit, i threw these in.
Quins - Flat hp quins, extra hundo HP to start helps with jungling, and also works well with Atmas.
Boots - Simple, Merc treads or Ninja tabi, go off of what the other team is playing, adjust ur masteries accordingly, and choose ur boots accordingly as well.
Bloodthirster - I rush this, since its 100 damage and 25 life steal, which is EXACTLY what he needs to start. In tiger stance at rank 5 at level 9, twisting he already has 100% atk speed bonus, a stun, a decent absorb. If you are able to get a bloodthirster soon after, you will have a massive lead on anybody else in the game. your AD will around 200 when u get full stacks, and with tiger stance, thats already 600 damage just on activation. At this point in the game, thats half a squishes HP. Also just gives u alot of survivability with the massive life steal in any stance, but coupled with stance twisting into turtle, one crit and u get like 1/6 of ur max hp back.
Phage/Frozen Mallet - This double dips for the reasons to get it. First off, all you'r tiny tiger stance hits, coupled with Bear stance means nobody, is getting away from you at all. Period. Secondly, give you a massive boost in HP, which adds survivability, and gives you a nice boost in atmas impaler damage. Very very good item for Udyr.
Atmas Impaler - Some say this item sucks, but it couldnt be more perfect for Udyr. He gets 99/hp per level base, which is high for champs, and makes Atmas worthwhile. Also it synergizes well with Frozen mallet to give extra damage. Having well over 3k HP means this will be a very cheap, and very good amount of damage, which boosts Tiger stance activation damage all the more.
Phantom Dancer - If somehow the game goes this long, and you get your six item, i chose Phantom dancer over Guardian angel since it simply synergizes so well with Udyr. Attack speed, although not needed, still helps alot while in bear stance/turtle stance when your twisting stances. Crit, well since we got Inifinity edge, crits part of the build, and with atmas, and Phantom dancer, crits will be common. Dodge, with ninja tabi, passive, and masteries means Nimbleness will proc ALOT. Also this will give him over 50% dodge with ninja tabi while stance dancing if you went for runing dodge. Finally gives that much needed Movement speed. This is much like atmas, and frozen mallet, have offensive qualitied to them, but also have defensive qualities to them. Udyr isnt meant to be a glass cannon, and to make him so would be shame.
So yes, that's burst DPS Udyr. Late game, its uncommon to do less then 2k damage in about 3 seconds to a squishy, and thats not an exaggeration. You will have close to 400 attack damage, and with tiger stance activation, that alone is 1200 damage almost in 2 seconds. Not to mention, you will be attacking with something close to a 70% chance to crit for 250% damage during those 2 seconds. Since you will be tiger stance attacking for 120ish a hit, thats 300ish damage per crit on ur mini hits. Your turtle stance/bear stance hits will crit over 900 damage about.
Quick how to gank with Udyr.
Bear stance in on them, movement speed = surprise. Stun, Twist into Tiger stance for the activation damage, get off a set of tiger stance attacks, then quickly switch to turtle. If they are still alive, switch back to bear to stun em since they will be attempting to run most likely, stun again, switch to tiger again, and just to continue to stance dance/twist your stances to keep your passive up, and rinse and repeat till dead. Between your life steal, absorb shield, stun, ridiculous damage, high HP, and dodge with defense armor/mag res, you're one incredibly deadly opponent.