This achievement is for killing twenty survivors or zombies with a shot to the head. It's cumulative so you don't have to do 20 exclusively on either. 8 survivors and 12 zombies will net the achievement for example.
You'll obviously need a weapon for this and the higher power the better. Also having some spare ammo also helps as it's easy to miss headshots, especially against moving targets. I'd suggest getting all 20 of these on zombies as they're far easier to predict and won't end up shooting back at you.
First, find a town and begin searching buildings for a firearm. If you find ammo or a magazine for a weapon you don't have, pick it up anyways. That way when you find a weapon you'll be good to go. The best places to look for weapons in the fresh spawn area is log cabin type houses and police stations. Police stations almost always have a shotgun or pistol with some ammo. Be aware that sometimes you can find a pistol without a magazine. That's okay, you can still load a single round into the chamber until you find one.
Once you have a weapon and an okay-decent amount of ammo, your next step is to find a house or building with a lot of windows. Preferably on the bottom floor. Close all the doors, get your gun and inventory ready, and fire off a shot. Guns are extremely loud and the zombies in your area will come sprinting to your location. Luckily they can't open or break down doors so they will just surround your house and scream at you through the windows. This is the perfect time to start popping heads for the achievement. The zombies will come to you in mass and stand there for you to take your time with aiming. Don't worry about other players for now as you're well defended with a horde of zombies creating a barrier between you and them.
It shouldn't take too long to get 20 headshots and if you kill all the zombies but don't have the achievement yet then move further into the town or to the next one and repeat the process. It shouldn't take more than two hordes attracted by gunshots to get your 20.
Stay safe survivors.