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