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