Battle for the Pacific

As the online for this game is dead get a boosting buddy then:

set up a team DM, HQ, 50 point

While you are working towards doing your weapons kills simply make sure that your boosting buddy stands very close to you and you use the LT to "zoom" the iron sights and shoot.

I playtested this and as long as you are not using a Sniper Rifle or pistol YOU CAN STILL USE THE LT to zoom the iron sights.

The kicker is that any headshots that do not kill your opponent in one shot DO NOT COUNT.

More of a tip then a solution, but when going for this to save time you should multitask it with some of the other achievements. Light Gunner and Heavy Gunner work well. Just go for headshots when working towards those and you should also get progress towards Marksman.
My boosting partner Speak79 and I did this on HQ, CTF, 1 flag capture, so we had infinite respawns as long as no one touched the flag.
Maybe you can downsight and not void this achievement, but I didn't find it too hard to get hip fire headshots when you have a partner cooperating with you and standing still.
Getting a headshot from the side seemed to be the easiest way to get the one shot kill.
Good luck!