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