You can do this for any enemy, and it doesn't need to be in a row. You can scatter this out throughout your game run. This might be harder on the easy difficulties since the enemies die a lot easier. This is why it might be better to do this on your crushing playthrough. Wait until you are at a checkpoint with nearby enemies, find one and shoot him first with the handgun/pistol, then with a long run (machine gun) and then run up and punch the enemy. This should kill the enemy once the punch lands and if you want you can get killed and do this again.
Defeat 5 enemies, each one taking damage from a handgun, long-gun, and melee