After you finish with the last tower (the Data Processing Security tower) go to lift just right before the level exit and save the game. Keep this save game alive so you can farm this file.

Pick a weapon in your inventory and exit the level. Upon loading the next map, do not change your weapon and proceed to kill the big monkey strogg enemy before you approach the tram and exit this map.

Simply reload the save game from the Data Processing Security tower and repeat the tram map with each weapon and you'll bag all the achievements quickly.