Like the previous achievement, but you must get all headshots in one hunting trip. I would recommend playing through the game first, and steadily upgrading your accuracy skill. Once I was on level 4 of accuracy this was not very difficult. Use the Bolt Action or Single Shot Rifle in America, use the Zoom and Steady feature, and focus on shooting them right in the head.
Also, aim for the top portion of their head when you can, so if you miss it doesn't hit them at all. Let them scatter and then try again. And if you're not comfortable with a shot, do the same thing. Let them scatter, than find them again on the map and see if your next opportunity is better. I'd also recommend not going for more than 1 animal per hunting screen.