Lozzy's solution is right on, I just wish to add something more. The guns are:
You can do this on any map. I got some kills in Ranked matches and some in Player matches. I only needed the flamethrower and went to a Player match so I could pick Spire (the level with the flamethrower), got the kill but no achievement. Since most comments suggest that you can get this on co-op missions, ranked, or player matches, I would like to add that you may have to get them all in the same type of game (not the same game), meaning, all weapon kills should be done on Player matches, or Ranked matches. Do not jump from Ranked to Player like I did.
Just play it safe and go to Player Match, choose Spire (flamethrower) and An Invasion (RPG), and you will get all weapons.
Hope this clears things out to people having some problems.