You need to beat Tyler in the first match, then accept his offer of a rematch and beat him again. If you lose the first match but beat him in the rematch, the trophy will not unlock. It doesn't matter what warm up exercises each character does. The game checkpoints before the initial match (but not subsequent ones), so if you mess up, you won't have to redo all the training again; you can just select Continue from the main menu. The trophy will unlock when Tyler asks Carla for yet another rematch.
Solution taken from PlayStation Trophies:
https://www.playstationtrophies.org/game/indigo-prophecy/tro...