A fairly easy achievement, which can be done on any difficulty. Easily done on the second mission, Pathfinder. Play the mission on Greenhorn, and make sure to switch between all of your weapons. Start off by killing the guard by the tree with your pistol. Continuing on, you will get to a bunker with two enemies in it, which you could either use a frag to kill them, or use your Thompson or Carbine.
Eventually when you place the beacon and everyone begins dropping down, you will have to go through a house ahead to proceed through the level. In the house, there is only 2-3 enemies in there, so you can easily switch to whatever weapon you haven't gotten a kill with, and nab the achievement.