Here is the full list of all 41 STAR OCEAN: Integrity and Faithlessness trophies - there are 22 bronze, 16 silver, 2 gold and 1 platinum.
Obtain all trophies.
Obtain all battle trophies.
Beat the game on Chaos difficulty.
Encounter every enemy.
Catalogue every item.
Unlock all item creation recipes.
View Fiore's ending.
View Anne's ending.
View Victor's ending.
Obtain all battle skills and signeturgical spells.
Complete all quests.
View Emmerson's ending.
Defeat Ethereal Queen.
Create the most precious metal.
Create the most valuable naturally-occurring item.
Create the most valuable sorcerous item.
Create the most valuable mechanical item.
Create the most valuable medicinal item.
Create an item that you shouldn't.
Ascend to level 255.
Defeat Gabriel Celeste.
Obtain the vast majority of the roles.
View Relia's ending.
Beat the game on Universe difficulty.
Create the most valuable edible item.
Use an emote during a cutscene.
Complete half of all quests.
Obtain half of the battle trophies.
Start a second playthrough.
View Miki's ending.
Defeat General Alma in the throne room.
Defeat Thoras in the parallel dimension.
Encounter half of all enemies.
Catalogue half of all items.
Create an item.
Defeat Der-Suul in the Slaughtery.
Make a riposte.
Defeat Pavine in the Eihied Mountains.
Eradicate Eitalon.
Activate a reserve rush.
Flee from a battle.