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