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