The goal of this build is to make a hybrid of Phoenix and Udyr.
It does NOT focus on jungle phoenix, but instead it utilises the extra damage, and AOE of phoenix.

Pros:
1. Lots of damage.
2. Tanky
3. Gank ready!

Cons:
1. Very Blue Buff Dependant
2. Pure Jungle Phoenix is a faster jungle.

Enjoy!

Here's the route:

1. Start at Blue golem. You do not require a leash, but it certainly is helpful! Use smite on it, and a health potion.
2. Then move to the wolves, use turtle when you get lower than 50% health, and switch between it and tiger, use a health potion if necessary.
3. Move to wraiths next, and use another health potion if necessary, keep switching between turtle and tiger, tiger for damage, phoenix to gain health back.
4. Attack the red buff lizard. Use smite, and a health potion.
5. Then take down the golems, and make sure you get your health back, either with potions, or with turtle.

After jungle is where diversity comes in.

You can choose to gank someone, as now you have both blue and red. I recommend ganking middle, or whichever lane you're closest to.

When ganking: Pop ghost and hit bear mode, so you will be impossible to dodge.

Or, you can go back and buy Madred's bloodrazer to keep going on your build.

Or, you can counter jungle their jungler, and try to engage them. It's up to you.

Once it is mid game, you should be about level 6 or 7, with your wriggles lantern.
Make sure you get blue buff, and hold it throughout the game, as you should be using lots of abilities.
Now you can get dragon. Ward it with your wriggles, and go in. Use bear mode, giving you one stack of your passive, then hit phoenix right before you're about to hit the dragon, then hit tiger, to maximize your damage output. From there, cycle through phoenix and tiger, hitting phoenix just for one second for its damage buff.
Make sure you have smite to finish dragon off!
Now you can go back, as you will be low health, and from there try to coordinate more ganks, jungle, or counter jungle.

When you can, steal the other junglers blue or red.

By late game, you've gotten your warmogs, and atma's.

You are now a serious one versus one machine! With a ton of health, a ton of damage, a stun, and lifesteal, don't be afraid to take on anyone one versus one. Make sure you keep getting blue, though it isn't as necessary now, consider giving it to spellcasters. (Though Udyr is super mana hungry!)

Now you want to stay with your team. You present a serious challenge, as you're very beefy, with tons of health, good armor, good magic resistance, and lots of damage. Chances are, people won't focus you, and you can stun half of their team, deal out AOE phoenix damage, plus serious tiger damage.

REMEMBER:

Before going into a teamfight, hit phoenix, then switch to bear, get the stuns on people, then switch to tiger for maximum damage. After, cycle through those to keep all buffs active.

In short, stay with your team, and do your thing in team fights. You're likely to win if you stay together.

All of the items are pretty standard. Feel free to change up the boots. I like to use boots of mobility which make you jungle faster, and gank harder.

I chose attack speed runes, as Udyr works best with attack speed, while you get items to give you extra damage. By late game you should get up to 2.4 attack speed easily, and you'll be doing great damage. Feel free to sub in other runes if you like.

Smite is chosen as this is a jungle build.
Ghost is chosen to increase your ganking potential. You can swap ghost out for something else, but your ganks will be much better with ghost.

I like this build the most because it suits Udyr very well.

By starting in with phoenix, you gain one stack, when going to bear, you stun people and gain your second stack, and by tiger you gain your third stack, allowing you to do massive damage.

In short, it is the best way to damage as Udyr!

Enjoy! :)

Remember Udyr's lore:
The mystics of Ionia delve into the deepest mysteries of Valoran, pioneering the most inner depths of spirituality. Their adepts are some of the most devout proponents of enlightenment and harmony...but as is always the case, there are those who follow a very different path. Born in a grassy clearing under a red moon, Udyr has always been compelled by the primal drive within him. His will was not untempered, simply undomesticated. As a boy, he toiled on his father's farm, but he felt a much deeper connection with the mustangs that would graze in the distant fields than with the townsfolk who would visit. Oftentimes he was dragged into the house at night with a swat and a scolding when his parents would find him sleeping beneath the stars.

On the day of his sixteenth birthday, Udyr bade his family farewell and struck a path to the east, determined to shed the trappings of ''civilized'' society. Freed of the shackles of cultural expectations, Udyr tapped into a well of inner ferocity he hadn't known before. His feral senses roiled to the surface and he let them overcome him. It was at this point in his life that Udyr truly lost his humanity. Poachers and travelers who entered his territory did so at terrible risk, and rarely managed to leave it.

A monk on a long journey passed through his woods one day, and Udyr decided to scare him, leaping from a nearby brush. The monk casually turned and redirected Udyr to one side. Udyr, enraged, tried time and time again to best him, but the monk was unassailable. When Udyr was exhausted, the monk wordlessly beckoned him to follow, and together they walked in silence to the Hirana Monastery. The monks there took him in, and taught him to harness and control his animalistic fury...most of the time.

You are an animal! You are a beast! You can take down anyone :)