To get this achievement, you will need to grab the weapon cases which contain LMGs, If you go to Loadout and scroll through the Light Machine Guns, you will see which area they are in to make things a little easier. Once in the area, interrogate Lieutenants and collect intel caches to locate them.
There are two LMGs which aren't available from weapon cases, these are rewards for defeating bosses of a specific area. The Llamativo is available after beating Carzito in P.N. De Agua Verde and the El Baston is available after defeating Madre Coca in Tabacal.
After collecting the last LMG, the achievement shall pop.