This should be easy enough to do on Chapter 1. While doing this achievement, I was playing with Brawl and on easy. I have no reason to believe this method won't work if you choose a different difficulty or character, but keep those in mind in case you have problems.
About 2/3 of the way through Chapter 1, you'll reach a section where you're in a large room with the opposite wall blown out (the Laboratory (1-8) checkpoint begins right here I believe). In this room, you'll fight a total of 6 Jet Soldiers (3 when you first enter, the second 3 after hitting the switch). When fighting them, you'll first want to allow them to take robot form. While in robot form, they will occasionally use a hover attack. What you'll want to do at that point is to get under them, double jump, and use your melee at the peak of your jump. This will cause your character to do an uppercut with his weapon hitting the foot of the Jet Soldier. This should destroy the foot killing the soldier and the achievement progress counter should pop up in the lower right hand corner. Repeat 5 times and you'll get your achievement.
If all the Jet Soldiers get killed before you get your achievement, you can either continue through the level across the debris and hope to get it on the Jet Soldiers out there (few of them ever land out there though) or jump off the side and restart.