Completing the zombie album requires you to fight against all 35 zombie types in the game. These zombies are special because they have name tags above them while you are fighting them along with a purple health bar. If they have a red check mark on their name that means you have already defeated them and they have been recorded in your Zombie Album. If there is no red check on their name then it means this a zombie you have not defeated yet and need to kill to add to your zombie album.
Some zombies only appear on Hard difficulty so it's best to play on that for your first playthrough so that you won't have to backtrack. To check your progress for this achievement, press start, go to Juliet's Stash then press.
Refer to Rep's Lollipop Collectibles & Zombie Album Guide to help you locate and slay them all!