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