We Are Legion - Killing the Officers
To be clear, there are four people you need to kill. You need to take out Major Polatli, Tech Sergeant Reyes, Dr. Richards and Quartermaster Mayes.
Note that there are options for stealth kills, and I have to assume that that's your goal. I can't really imagine handling an entire camp of leveled NCR troopers and rangers. If you plan to do it, remember to pickpocket as much ammo as you can first (use a disguise if you have to do so) and try to find a good post where they won't be able to get behind you. Take out dogs before they can rush you and try to put troopers down fast before their service rifles tear into you. Technically you will only trigger the entire camp to attack if you openly attack Quartermaster Mayes. In other situations, the response should be limited.
Dr. Richards should be the easiest kill. He goes to sleep in an isolated tent and is by himself all day in the Medical Tent. If you've got Mister Sandman or if you're good with the silenced pistol, you may be able to take him out in either tent without anyone noticing.
Quartermaster Mayes should also sleep, so you can go for a Mister Sandman kill. He's also by himself in his tent, so if you've got a good silenced pistol or a lot of points in Sneak you might be able to pull off a stealth critical miracle. Since he's along, just reverse pickpocketing a grenade might work (although he's very sensitive to pickpocketing). An all out attack is ill advised, since the entire camp will respond and you're best hope will be to retreat after kill him.
Major Polatli actually isn't the hardest to kill, just because he should wander around a bit and also sleep. It will be almost impossible to easily kill him in the command tent though, unless you get lucky with C4.
Which brings us to Tech Sergeant Reyes. She's the hardest to kill, because she never sleeps and never leaves the command tent and the safety of the two soldiers inside. The best option seems to be using C4. Either pickpocket it onto her or leave it on the floor. Then just go somewhere you won't be seen and start sneaking. Use the detonator to kill her, and potentially Major Polatli if you get lucky with the C4 blast. You should be able to find some C4 in a locker by the NCR blockade along the road to Nelson, or you can just buy some from Mick and Ralph's secret stash in Freeside.
Regardless of how you manage to pull it off, report your success back to Dead Sea and collect "Liberator" as your reward. This unique machete is a little underwhelming considering your work, but it's for the greater glory of the Legion.