Here is the full list of all 30 Army Corps of Hell trophies - there are 12 bronze, 12 silver, 5 gold and 1 platinum.
Alchemized first equipment for magi.
Crushed 100 foes.
Alchemized first equipment for spearmen.
Alchemized first equipment for soldiers.
Cleared the first stage.
Obtained all trophies.
Cleared up to stage 20.
Cleared a stage between 11 and 20 with soldiers only.
Cleared a stage between 11 and 20 with spearmen only.
Cleared a stage between 11 and 20 with magi only.
Cleared a stage between 11 and 20 with an overall platinum rating.
Cleared all Purgatory stages (21-30).
Cleared a Purgatory stage (21-30) with soldiers only.
Cleared a Purgatory stage (21-30) with spearmen only.
Cleared a Purgatory stage (21-30) with magi only.
Cleared a Purgatory stage (21-30) with an overall platinum rating.
Cleared all Tartarus stages (31-40).
Cleared a Tartarus stage (31-40) with an overall platinum rating.
Exceeded 66,666 jewels in your possession.
Achieved an overall platinum rating ten or more times.
Achieved the maximum rating (excellent) in one of the musical instrument mini-games.
Crushed 1,000 foes.
Crushed 3,000 foes.
Defeated all bosses.
Completely filled the Demonic Compendium.
Alchemized all consumable items.
Alchemized all weapons and armor for soldiers.
Alchemized all weapons and armor for spearmen.
Alchemized all weapons and armor for magi.
Alchemized all possible weapons, armor, and items.