update: my solution is a bit outdated, because it's possible to load a checkpoint after landing a headshot and doing this over and over again until you unlock the achivement. My solutions shows you the "in one go" way. Feel free to use any method that works best for you.
begining of the original solution:
There is one thing you have to know to make this achievement way easier. You can and should turn off "Controller Auto-Aim" in the settings. Now play on easy and take your time. I got this achievement in the third chapter "The Raid", in the room where you have to activate the fire alarm.
I recorded a clip for all of the players who prefer a video:
There are probably many other parts during the game where you can pull off the 20 headshots. If an enemy kills another it doesn't break you kill streak. Feel free to leave a comment and i'm happy about any feedback!