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.
Complete half of all quests.
Encounter half of all enemies.
Catalogue half of all items.
Make a riposte.
Flee from a battle.
Defeat Der-Suul in the Slaughtery.
Use an emote during a cutscene.
Defeat Pavine in the Eihied Mountains.
Create an item.
Activate a reserve rush.
Eradicate Eitalon.
Obtain all trophies.
Defeat Thoras in the parallel dimension.
Defeat General Alma in the throne room.
Defeat Gabriel Celeste.
Defeat Ethereal Queen.
View Miki's ending.
View Victor's ending.
View Fiore's ending.
View Emmerson's ending.
View Anne's ending.
View Relia's ending.
Start a second playthrough.
Ascend to level 255.
Beat the game on Universe difficulty.
Beat the game on Chaos difficulty.
Unlock all item creation recipes.
Create the most valuable medicinal item.
Create the most valuable edible item.
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 an item that you shouldn't.
Obtain all battle skills and signeturgical spells.
Obtain the vast majority of the roles.
Obtain half of the battle trophies.
Obtain all battle trophies.
Encounter every enemy.
Catalogue every item.
Complete all quests.