Here is the full list of all 24 Beast Quest trophies - there are 6 bronze, 11 silver, 6 gold and 1 platinum.
Unlock 10 Iron Chests.
Unlock 10 Bronze Chests.
Meet Silver and have him join you.
Complete the Sword Cookies side quest.
Meet Elenna and have her join you.
Complete all of the other trophies.
Complete the game on Beast Master difficulty.
Free all four Beasts of Avantia.
Purchase all upgrades for Tom.
Call all Allies in combat at least once.
Complete all Side Quests.
Free Ferno the Fire Dragon.
Free Nanook the Snow Monster.
Free Arcta the Mountain Giant.
Complete all Hunter’s Marks.
Complete a Hunter’s Mark.
Complete the Beastologist side quest.
Complete the Pet Rock side quest.
Defeat 500 enemies in total.
Complete the Awful Wizard side quest.
Unlock 10 Gold Chests.
Get 50 Perfect Dodge Bonuses in combat.
Get 50 Multi-KO Bonuses in combat.
Get 50 Flawless Bonuses in combat.