Here is the full list of all 44 Nuclear Throne achievements. It takes around 200 hours to unlock all of the achievements on Windows.
Reach 7-3 on a Daily.
Defeat the Technomancer.
Defeat Hyper Crystal.
Defeat Mom as Rebel.
Defeat Mom.
Reach Level Ultra as any character.
Reach the Nuclear Throne in under 10 minutes as Plant.
Unlock a Crown as any character.
Unlock a Golden Weapon for every character.
Defeat the Nuclear Throne.
Loop past the Nuclear Throne.
Loop the game.
Defeat Throne II.
Eat a Hyper Weapon as Robot.
Reach the Nuclear Throne.
Reach 6-1.
Defeat Lil Hunter.
We hereby sincerely apologize.
Reach 2-? as Eyes.
Reach 5-?.
Defeat Horror.
Reach 3-?.
Reach 3-1.
Reach 5-1.
Unlock a Golden Weapon as any character.
Defeat Big Dog.
Die.
Reach 2-1.
Defeat Big Bandit.
Loop as every character.
Reach 4-? as Crystal.
Reach the Nuclear Throne with Melting without choosing Rhino Skin or Strong Spirit.
Defeat the Technomancer as Steroids.
Reach 2-1 on Hard Mode as Chicken.
Defeat Hyper Crystal as Horror.
Defeat Captain as Rogue.
Unlock a Golden Disc Gun or Golden Nuke Launcher.
Reach Level Ultra as Skeleton.
Play as Frog.
Sit on the Nuclear Throne as headless Chicken.
Unlock all Crowns as one character.
Unlock Hard Mode.
Defeat Captain.
Get 100% of the unlocks.