This isn't as difficult as it may seem and can be easily unlocked on the first level within a few attempts.
From the starting point of level 1:1, move to the lower left section of the level. Here, you will find four GI Pups walking around. The only slight issue here is that the most-left Pup stays quite close to the left side of the screen. Be careful not to stand still on the green cheese near this section and time your head jump on the Pup when he walks as far to the right as possible. Once he's been stuffed under his helmet, move to the left side of the Pup and punch him using
. Immediately start to walk to the right after the helmet so than the three Pups who are about to be killed by the helmet will all be on screen.
Here's a quick video showcasing the method in action: