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