Here is the full list of all 37 One Piece: Pirate Warriors trophies - there are 20 bronze, 13 silver, 3 gold and 1 platinum.
Completed the Brook story in Another Log.
Completed the Franky story in Another Log.
Completed the Robin story in Another Log.
Successfully performed an event attack on Lucci.
Successfully performed an event attack on Bruno.
Completed the Usopp story in Another Log.
Successfully performed an event attack on Crocodile.
Retried an Episode.
Fell into the water or off platforms 10 times.
Collected all the coins featuring powerful enemies.
Completed the Sanji story in Another Log.
Completed the Chopper story in Another Log.
Successfully performed an event attack on Arlong.
Completed the Nami story in Another Log.
Completed the Zoro story in Another Log.
Defeated 1000 enemies in a single Episode for the first time!
Activated your first skill.
Stunned an enemy for the first time by attacking their weak point.
Successfully performed an event attack on Don Krieg.
Successfully performed an event attack on Buggy.
Performed your first Crew Strike.
Cleared the first stage.
Successfully completed your first action with Luffy.
All Trophies acquired!
Successfully performed an event attack on a Pacifista.
Successfully performed an event attack on Aokiji.
Successfully performed an event attack on Akainu.
Collected all the coins featuring the Straw Hat Pirates.
Collected all the coins featuring members of the Navy.
Completed Marineford just as it happened in the original story.
Completed the Ace story in Another Log.
Completed the Hancock story in Another Log.
Completed the Jimbei story in Another Log.
Completed the Whitebeard story in Another Log.
Activated all skills.
Cleared the Main Log.
Defeated a total of more than 100,000 enemies.