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.
Flee from a battle.
Defeat Pavine in the Eihied Mountains.
Eradicate Eitalon.
Activate a reserve rush.
Create an item.
Make a riposte.
Obtain all trophies.
Defeat Der-Suul in the Slaughtery.
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.
Use an emote during a cutscene.
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 half of all enemies.
Encounter every enemy.
Catalogue half of all items.
Catalogue every item.
Complete half of all quests.
Complete all quests.