Here is the full list of all 26 Quest of Dungeons trophies - there are 7 bronze, 12 silver, 6 gold and 1 platinum.
Beat Game in Hell
Listen closely
Beat Game with Wizard
Find 50 hidden stash
Beat Game in Hard
Beat a Custom game in Hard or above with 10 floors
Beat Game with Assassin
Purchased all stock from a shopkeeper
Complete 50 quests
Beat 20 Bosses
Beat Game in Normal
Beat the Rackan Mansion
Beat Game with Shaman
Beat Game in Easy
Beat Game with Warrior
Disarm a trap that has loot!
Unlock Chest
Beat a Boss
Unlock a door
Complete a quest
Complete all Trophies
Beat Game in 30m
Pick 500k Gold
Defeat 3 ghosts of a past Hero
Beat Game with NecroDancer
Do 1000 points in KC NG N P (L R X)