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