Here is the full list of all 20 ZOMBI achievements worth 1,000 gamerscore. It takes around 20-25 hours to unlock all of the achievements on Xbox One.
Kill 200 zombies
Survive the Ambush at the Church
Get the XXL BOB
Get into the Nursery
Get into the Tower of London
First Kill with the Crossbow
Kill your first zombie with a Molotov Cocktail
Get the XL BOB
Kill 50 zombies
Kill 100 Zombies
Get into Buckingham Palace
First Headshot with a gun
Reach a Survivor Score of 2000 points
Get into the Supermarket
Pick up a backpack (Bug-Out-Bag)
Make it to the Safehouse
Hack all of the CCTV junction boxes in London
Finish Game in Chicken Mode
Finish Game in Standard Mode
Finish Game in Survival Mode