The Whack-a-Cody minigame can be found about halfway through The Depths of the Shed — you can’t miss this minigame because Dr. Hakim essentially forces you to play it.
May will stand on top of the box with her hammer. Cody must get inside the box. Basically, the two of your are playing whack-a-mole. Cody pops up using the left stick and May must aim at Cody and press RT/R2 to hit Cody.
May gets +2 points for each Cody hit. Cody gets +1 points for every (basically) half-second they remain popped up. Whoever fills their bar at the top of the screen first wins.