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