To get this achievement, you must get 47 precision headshots using a sniper rifle. A "precision" headshot means that you have to hold the trigger down very slightly to steady your aim, hold your breath, and slow time before pulling it all the way to shoot. Doing this takes a little bit of practice but you can get the practice going for this achievement.
If you wait until the last mission, Absolution, you start with a sniper rifle and plenty of targets. Start the level and use up what ammo you can before reloading the checkpoint. Continue to do this and you'll have it eventually. Just remember that you need to steady your aim first or it won't count.
