Can be achieved quite early on.
You can get a really good start on this on the first level. While on the boat you start with only the pistol and the zombie are in a "tutorial" mode, where they are fewer between. Just stand and shoot, after about 2-3 shoots you will get a headshot kill.
With enemies which crawl, crouch and shoot. As the game progresses, you will have enemies which jump and enemies which horde up, so a pistol approach is difficult. Your next best friend in headshots is the Magnum. This can multi-headshot kill and will get you out of tight spots with running zombies and larger groups.