Tryndamere has a hard time dealing with champions that can chunk him down low, and then zone him of cs, not letting him build fury/ heal. Majority of bruiser and juggernaut roster can do that, since they usually have enough damage to quickly pop tryndamere, and they get pretty tanky, so Trynd does not kill them fast enough. Tryndamere also has hard time dealing with ranged champions that can blind / kite him and burst hard — Quin, Teemo.
There is one thing to keep in mind though if you are playing a bruiser. Don't fight Tryndamere when he is at his strongest, especially in the early game. He has really good early base stats compared to most melees, but most bruisers will start beating him early to midgame if they play / itemize correctly, as long as they don't let Tryndamere get a ahead in the early game.