To get the Achievement, you need to get a "First Strike" Medal, which means get the first kill in a match. (Please note it only works in Matchmaking, NOT THE FIREFIGHT GAMETYPE!)
I got it when playing Team SWAT, no shields so Headshots are instant kills/ So just select the Team SWAT PLAYLIST and hope for the best.
If you don`t want to do it in SWAT, just continue playing any Gametype and try to get the Power Weapons (Sniper, Rocket, Plasma Launcher etc) and try to lure an enemy towards you while you have a Power Weapon.
This is now much easier done in the Living Dead Playlist (Zombies), there are 3 rounds in which you can earn 3 First Strikes in total, so a pretty high chance to get it. My tips are when you spawn as a Survivor equip your Magnum and try to headshot the first Zombie in sight, you will headshot him with one shot because shields are disabled for the Zombies, and if they get close, shotgun them back to where they came from! (Best maps to get Headshots on are Powerhouse, Countdown, Boardwalk and The Cage.
Thats all I can do, good luck.