This is pretty simple if you have good aim. Just make sure your killing blow hits the head of enemy NPC's.
You can get headshots with firearms, energy weapons, and melee weapons.
You can not get headshots using explosives or barrels.
They show an example of headshots in one of the load screens: You know you have a headshot when the damage indicator turns red.
If you are missing shots, then you can upgrade the bullet spread on your weapon in the backpack.List of Specific Zombie Headshots
Further enemy details are put on the next grade of headshot achievements in order to avoid spoilers.
Woodland enemy types are explained in the 'Hotshot' achievement.