You need to take your time on the SOFLAM. If you rush too quickly to take out the large targets, you lose the ability to keep firing and won't be able to finish off the infantry. Leave one of the closer camps for the end as it will be easier for you to see where to place the shots.
At the beginning concentrate your fire at the furthest targets and just lay down a ton of fire from all 3 weapons. The 3 weapons do not share the cooldown timer with each other so you can really tear it up that way. Keep an eye on muzzle flash as it is hard to see some of the infantry from a distance.
If you're taking too long, Reaper will tell you they are RTB (return to base). The good thing is that they will keep saying it for a while and you can keep shooting. So if you hear it, know that you need to hurry up, but you still have some time if you're close.
If the achievement doesn't pop when you lower the SOFLAM, just reload your last checkpoint as there is no fighting between this part and the previous checkpoint.