It's always worth it.
Never focus Tryndamere.
Never focus tanks.
Both jungles are yours.
Umad. Very very mad.
If the tower is below half health, you can always take it.
As in my other builds, I strictly encourage tier 3 Vampirism runes even though I can not advertise them. I will answer and try to help those who comment.
This build may take some practice because you probably have lesser sustain compared to other AD Carries and you might be more used to Tankier champions who are safer. But he is fun overall and is a great pick if you want to play a constant rager.
This is my general core build for Jungle Tryndamere. Items can be removed and replaced situationally, but ideally this is what you try to aim for.
Tryndamere, as I perceive him is a mainly attack speed oriented champion. Which is why I don't understand some of the builds on here. His rage bar fills per hit and per kill. He can heal by using his bar and he passively gains critical strike chance because of his bar. Therefore, being able to fill your rage quickly after being used should be a good thing.
While some may disagree with me you can take this build however you like it but if it helps feel free to use it.
Pros / Cons
Less damage per hit. This is not a 1.8k damage per hit build. Even though you may want those kind of builds This build fits Tryndamere better in my opinion.
Nearly maxed attack speed and critical chance. This build will give you about 2.3 hits per second and 95% critical strike chance.
Almost no tankyness. Tryndamere all around is not a tanky champion nor meant to be built like one so there is no Frozen Mallet or Warmogs.
Heavily based upon CS. While you can get fed off of ganks and kills this is CS based build.
You are not a Team fight oriented champion you are more of a 1v1 ganking champion or split push champion.
Smite is always a must for jungling. I use it for all of my jungles, and when playing randoms it's the universal symbol nearly everyone recognizes for a jungler.
The second spell is your choice. I like Ghost to help with successful ganks and to cross the map quickly. Paired with the movement speed you'll build early on its great.
Flash can be used if you need to pass over two walls at one time to save yourself. (Spinning Slash over the first.)
Exhaust is a nice choice to help take down particularly strong enemies or to slow a target if your mocking shout has been used already.
Start at Wolves and clear the entire camp then go take Blue killing the big Golem first and smiting it then clearing the smaller creeps. After blue take Spinning Slash and go through the wall and make your way to Wraiths. The CD on Spinning Slash should be up by the time you reach the corner adjacent to Wraiths. Stand next to it and Spinning Slash through the wall into the center of the camp and kill them in te random order you start auto attacking.
Walk to the wall closest to you that protect the Red Buff and Spinning Slash through it and kill the smaller Lizards before the biggest one. Bloodlust heal if you need to. Spinning slash through the wall on top of the Golem camp and kill the biggest Golem first. Run towards the wraith camp and by the time the camp come in sight the wraiths should spawn back up and you can Spinning slash into them and kill them. Go to Wolves and clear the camp and go to your first gank. Recall afterwards (DO NOT DIE) and buy or continue Jungling. You want to stay out until you can buy Boots of Speed and Zeal.
After this you need to stay in the jungle as much as possible while ganking periodically to keep the enemy on their toes and to make your presence known. Focus ganks towards top if it's 2v1. Farm the jungle and buy according to the guide while keeping an eye on the map and placing wards on the river. By the time you get your first or second Phantom Dancer you can take Dragon. If not then Spinning slash out of the dragon camp so you don't die and try again in a few levels.
Team Play / Tips
You are squishy AD DPS and because of that and how strong you are and can become, you will get focused. So do not be the first into a fight. Use your ult only when you know it will benefit you. Focus other squishies in team fights.
Your best bet though is to catch enemies alone and take them on 1v1. If you have farmed accordingly you should have one of the highest, if not the highest, CS. Focus on taking Dragon and split pushing towers. Clear the enemies jungle, any chance you get, to hinder them.
Tips: Tryndamere is potent with champions like Shen and Rammus that have a taunt so that they are attacked instead of him. He can heal damage he takes while the enemy is taunted and refill his rage bar quickly with this attack speed build. This can eliminate him using his ultimate so frequently.
You can turret dive at full health to take an enemy with a partner if you time your Undying Rage, Spinning Slash, and Bloodlust right.
Because of Spinning Slash you are one of the quickest Junglers because half of the jungle is just a set of walls you can easily fly over. This plus the paring of his overall kit and this build make him one of the most efficient Junglers/Gankers I have seen so far with the current jungle, if used correctly that is.
This is a great build because you can buy the pieces pretty cheap to start with incase your prone to dying with Tryndamere and you still want to be useful.
It generally enhances almost all of his unique characteristics and it works better than some builds focused around an Infinity Edge Blood Thirsters and a Frozen Mallet.
Any Tryndamere players should try this build out if not for the fact you don't know him well then for the fact it might be more enjoyable for you.