UPDATE: Thanks to 'General Wizzard' for confirming, you can lock the Marines behind the 1st or last doors by playing coop and having your partner teleport you forwards and still get the achievement.. makes it much easier!
UPDATE 2: I just did this with two friends(Nov 1, '15); What we did was go until we met the first marines, then advanced a little to the next enemies trying to figure out who the Marines were following. Turned out to not be the host. The person they were following stayed back with the Marines who didn't budge at all, and the other two of us continued, cleared out the rest of the first area, and teleported him through the door. Achievement popped for both of them first try! (It was on Easy, no skulls)
This achievement can be rather tricky, simply because the Marines like to get themselves killed by going out into fire. I highly recommend doing this with more than one person in coop, and on EASY!
You can have one person hang back and keep the Marines from running forwards into the kill zones as they die in about one or two Carbine shots. However, if you do this, you run the risk of having whoever is in the lead teleport you forwards past a closed door and into a checkpoint, so make sure you brings the Marines forwards to each gate that opens and closes.
However, we did confirm that you don't have to bring the Marines through the LAST door that opens and closes. My partner RoboFailBoat teleported me through that door, when we had only one Marine left, the Marine was behind that door and we got the achievement!
Could someone please try teleporting past the first door and trapping Marines behind the first door and see if that counts for Marines alive--if it works like that, it makes this EXTREMELY easy!! Please let me know if it works!
Thanks for testing and confirming it works for the first door 'General Wizzard'!