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