To add to the above solution, a good place to do this is in chapter 3. As soon as you learn how to do a gun scout hijack, there is a mech to the left that you can kill (if you didn't kill it already, just avoid shooting it with your staff and let trip distract it instead).
Shortly after that, and following a cut scene (trip will say whoa, there's a lot of mechs out there) you will see a mech with a shield to the left. Approach it, stun it, and then attack it a few times so that you can rip off it's gun (just wait for the B button to pop up). After you get the gun, three mechs will charge at you, and one will call for reinforcements (which will spawn two more mechs). Once you kill all five mechs, just reload the checkpoint, then rinse and repeat to get the achievement.