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