Here is the full list of all 15 King Oddball achievements.
Complete all One Rock Levels.
Complete all Grenade Levels.
Find and complete the Secret Moustache World!
Gain five extra rocks during a level.
Complete the Stash!
Kill the King.
Complete a level with one rock and gain more than one extra rock.
End the World.
Hit the King with a rock three times during a level.
Destroy six enemies with one throw.
Throw a thousand projectiles.
Destroy a thousand enemies.
Complete a level using only one rock.
Destroy four enemies with one throw.