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