Here is the full list of all 43 Battle Princess of Arcadias trophies - there are 30 bronze, 8 silver, 4 gold and 1 platinum.
Earned all other trophies.
Won the first boss battle.
Defeated a Dragon.
Defeated a Golem.
Defeated a Pharaoh.
Defeated a Lamia.
Defeated a Giant Spider.
Defeated a Giant Crab.
Stood victorious at the final battle.
Defeated 100 enemy units.
Defeated 500 enemy units.
Defeated 1,000 enemy units.
Defeated 3,000 enemy units.
Achieved a 100 combo.
Achieved a 300 combo.
Achieved a 500 combo.
Defeated 1,000 enemy units with the main character.
Reached Level 99 with one character.
Reached Level 99 with all characters.
Won a battle without using a single item.
Cleared a combat session without swapping.
Sold items on 100 separate occasions.
Bought items on 100 separate occasions.
Had over 500,000 G.
Enhanced a weapon for the first time.
Performed 100 weapon enhancements.
Upgraded a weapon into a new weapon.
Upgraded 10 weapons.
Upgraded 30 weapons.
Obtained 100 weapons.
Obtained 500 weapons.
Obtained 50 accessories.
Trained a brigade for the first time.
Won your first skirmish.
Won every unique skirmish.
Won 100 skirmishes in total.
Recruited every character to your cause.
Achieved max Honor for one character with one other character.
Achieved max Honor for one character with all other characters.
Achieved max Honor for all characters with all other characters.
Won every possible battle.
Achieved S-Rank in a battle for the first time.
Achieved S-Rank in every possible battle.