Here is the full list of all 20 ZOMBI achievements.
Get into the Supermarket
Pick up a backpack (Bug-Out-Bag)
Make it to the Safehouse
Kill 50 zombies
Kill 100 zombies
Kill 200 zombies
First Headshot with a gun
Kill your first Zombie with a Molotov Cocktail
First Kill with the Crossbow
Get into Buckingham Palace
Get into the Tower of London
Get into the Nursery
Survive the Ambush at the Church
Get the XL BOB
Get the XXL BOB
Hack all of the CCTV junction boxes in London
Reach a Survivor Score of 2000 points
Finish Game in Chicken Mode
Finish Game in Standard Mode
Finish Game in Survival Mode