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 4-? as Crystal.
Unlock a Golden Weapon as any character.
Reach the Nuclear Throne.
Unlock a Crown as any character.
Defeat the Nuclear Throne.
Reach 6-1.
Reach Level Ultra as any character.
Defeat Lil Hunter.
Reach 5-?.
Reach 3-?.
Reach 2-? as Eyes.
Defeat Horror.
Reach 5-1.
We hereby sincerely apologize.
Defeat Big Dog.
Reach 3-1.
Reach 2-1.
Defeat Big Bandit.
Die.
Loop past the Nuclear Throne.
Loop as every character.
Reach the Nuclear Throne with Melting without choosing Rhino Skin or Strong Spirit.
Reach the Nuclear Throne in under 10 minutes as Plant.
Unlock a Golden Weapon for 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.
Defeat Throne II.
Defeat Mom.
Defeat Hyper Crystal.
Defeat the Technomancer.
Unlock all Crowns as one character.
Unlock Hard Mode.
Loop the game.
Defeat Captain.
Get 100% of the unlocks.