In the Army Men Challenge booth, you will come to the Block Breakout Assault (not to be confused with the Midnight Breakou mini game).
Just keep hitting all the balls that are being shot at you. You will notice that some of the ball colors will repeat which is fine, the description doesn't mean hit different colored balls. Try to avoid hit the balls that bounce back at you or bounce off the star bumpers. As those will not count for this achievement.