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