Corridor Z

Headshots are instant kills on normal zombies, and are achieved by allowing them to get close to you before shooting them with a weapon. You can start a run with a weapon by using the Armed Start perk, and you can pick up weapons off the ground when they appear (look for a red glow).

This is cumulative across all playthroughs, and should come naturally as you complete missions for collectibles, as many missions require killing zombies. Focus on headshots to both preserve ammo, and work toward this trophy.