Precision:

Conquerer:

Its a must have on Tryndamere jungle, especially this build because it converts 20% of your damage to true damage, that means no matter what you do 20% of your damage on your opponent. This is especially good with this build because when you have the 100% crit chance you do 400+ damage on 1 hit already with full fury.

Triumph:

Is pretty self-explanatory because the other 2 dont work that well on Tryndamere + Triumph makes you able to kill mutiple people easier because you get health back on a kill.

Legend Bloodline:

For extra lifesteal in the early game so you can survive camps a bit better and since bloodline got sort off a buff last patch you are going to get 12% lifesteal when you complete it which is alot. You could also take Alacrity but I think bloodline is better.

Last stand:

Its really good combined with his ult + conquerer, it makes you do 11% extra damage when you are on low health (Which you usually are when you ult) so you get 11% extra damage on top of the 20% true damage. The other 2 runes on this path could also be viable but I think last stand just works really well with his ultimate.

Inspiration:

Magical boots:

It is 300 free gold and in this build you won't be getting your boots anytime soon anyways so its nice to have them for free <10:00 min in + On top of that you are getting. 10 extra ms which may not sound much but combined with your W and approach velocity it could make that little of a difference between hitting your opponent and them running away.

Approach velocity:

It is an absolute must have when you are jungling in my opinion because it makes your W so much more powerful that you dont have to max it out until your last few levels.

Other inspiration path runes:

The only other 2 viable runes for this path in my opinion are Future's market and Cosmic Insight, This build has some pretty expensive items and after you back the 1st time you might not always have 1300 gold to buy the B.F sword so if you want to play it safe you could switch out magical boots for Future's market so you could reach your spikes earlier but its up to personal preference of course. Cosmic insight for extra cd so you can use your abilities more often but in my opinion it isnt that good on tryndamere since your abilities cooldown is not that high anyways.

Offense, Flex and Defense runes:

Offensive + Flex:

Adaptive force 2x for the extra damage. You could run attack speed in the Offense slot but you are going to build quite a bit of attack speed later on anyways.

Defense:

I take health because it means you can have a little bit more health left when you hit your extra AD with your Q. But you could also take the armor or magic res depending on your opponents matchup.

Bloodlust is Tryndameres go to ability for jungling because it gives you health back plus extra ad when low on health it is imo pretty much tryndameres go to ability, then after I take spinning slash because of the 100% crit build you are going to get that 1 second cd on every hit so you can use it more often + lowering the cd of the ability itself even more is going to make you a beyblade across the map. W last because it is good enough to have it level 1 in my personal opinion.