Armor items such as Thornmail and Randuin’s Omen do extremely well against Tryndamere because he is completely auto-attack based.
Igniting him at the end of his ultimate duration will usually end up in a kill, as his healing from his Q will be halved.
Try to turn around when Tryndamere is casting his Mocking shout to save yourself from getting slowed.
If you have the tools to do so, try to zone him out of any possible fury. His 35% crit passive can turn almost any fight around. Tryndamere has a relatively weak early, so don’t be afraid to get in his face.