Before you can go for this Achievement you need to find all the Bolt Action Rifle parts which you will find in strongboxes, you will need the lockpick. If you do not have the lockpick then you need to head to Logging Camp in Soviet Installation. You will find a man there who needs you to take down some transmitters, once you do that for him he will give you the lockpick. Once you have the lockpick you can go and get the Bolt Action Rifle parts. There are one or two guides online stating which strongboxes which weapon parts are in, IGNORE THEM. I wasted hours following these guides, the weapon parts are completely randomised so you are best off just going after all strongboxes until you get the weapon parts you need. Once you have all the Bolt Action Rifle Parts head to a campfire to unlock the weapon.
Now you just need to equip the weapon and get 25 headshots. An easy way to do this is to play in Expeditions mode, Chapter Replay Elite, The Acropolis, Adventurer Difficulty. Get to the campfire, double check your Bolt Action Rifle is equipped. Seconds later a cutscene will play and you will be in an area with five or six enemies, take them all out with headshots and then reload checkpoint, rinse and repeat until achievement pops, took me less than five minutes.