During the mission, just before you acquire a King Chim Chim, hit Select to bring up the map. Press O to exit the map and snag the King immediately after the map disappears. If you do this correctly, when you get the King Chim Chim, you will instantly acquire all three of the necessary Kings and finish the mission. You can make the glitch easier to accomplish by pressing X right after O, but doing so may bring up the Mission Info text box. Press O to clear it before returning to town, or you will be forced to reset the game.