When playing sniper in eternal mode or coop, headshots with any primary or secondary counts for this.
A tip to speed it up and if you are having problem getting headshots in chaotic gameplay is to play the first trial (stealth).
You get an smg and it's easy to get in a bunch of headshots from the enemies spawning in during the trial mission. Got the achievement in around 10 minutes.
The trials can be found in the armorer menu and from the looks of it all class related achievements can be done in trials quick and easy.