This epic quest requires you to get 10 headshots with rifles.

This includes any type assault rifle with any rarity. It is easier to pull of headshots if you have a good vantage point over your opponent. You should build a fort to get yourself in a good position. It also helps if the opponent is not too far away. The accuracy of assault rifles is not great, especially makeshift and primal varieties, so if you can get quite close to make this easier.

Crouching and standing still increases your accuracy so make us of this to increase your chance of making the headshot. The first shot you take is also more accurate so if you have the drop on your opponent try and wait for a good opportunity to take the first shot. If they are standing still this will make it a lot easier.