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