First off, I strongly suggest you play through each booth in Free Play (after getting your co-op achievement out of the way...) as you have the ability to restart any minigame.
Each shooting gallery gives you 2 power ups. One before and one after the pies are thrown at you. It seems the 2nd one is the random one and more commonly the 1st power up is the same each time you replay the level. I suggest using the Invasion of the Space Raiders
minigame in the Space Frontier booth as there are many more targets on screen than are needed for the achievement. Play the level until you are given the 2nd power up. If it isn't one of the ones you need, restart the level.
When you do get the power up, simply hold the the right trigger
the entire time which enables auto fire (which you probably use anyways) and swing your weapon of destruction across the orbs in the center of the screen. The achievement unlocks as soon as you destroy the 20th target using the power up.