Here is the full list of all 45 Nuclear Throne trophies - there are 31 bronze, 10 silver, 3 gold and 1 platinum.
Unlock a Golden Disc Gun or Golden Nuke Launcher.
Eat a Hyper Weapon as Robot.
Defeat the Technomancer as Steroids
Defeat Captain.
Defeat Captain as Rogue.
Reach 2-1 on Hard Mode as Chicken.
Unlock Hard Mode.
Defeat the Technomancer.
Defeat Hyper Crystal.
Defeat Mom.
Reach 2-? as Eyes.
Reach the Nuclear Throne with Melting without choosing Rhino Skin or Strong Spirit.
Reach Level Ultra as any character.
Loop past the Nuclear Throne.
Defeat Throne II.
Loop the game.
Reach the Nuclear Throne in under 10 minutes as Plant.
Reach 7-3 on a Daily
Reach the Nuclear Throne.
Unlock a Crown as any character.
Reach 4-? as Crystal.
Defeat the Nuclear Throne.
Reach 6-1.
Defeat Lil Hunter.
Unlock a Golden Weapon as any character.
Reach 3-?.
Reach 5-?
Defeat Horror.
Reach 5-1.
Defeat Big Dog.
We hereby sincerely apologize.
Die.
Reach 3-1.
Reach 2-1.
Defeat Big Bandit.
Completed Every Challenge We Could Think Of In Nuclear Throne.
Loop as every character.
Unlock a Golden Weapon for every character.
Defeat Mom as Rebel.
Defeat Hyper Crystal as Horror.
Reach Level Ultra as Skeleton
Play as Frog.
Sit on the Nuclear Throne as headless Chicken.
Unlock all Crowns as one character.
Get 100% of the unlocks.