Zombieland: Double Tap - Road Trip

Easier than actually going through levels. You need 2 controllers.

Load up Horde on the Not So Pleasantville map. You start next to the crane. When zombies start heading your way, launch the crane. That'll give you a ZKOTW nomination. Now let them rush you. You also get XP. Double tap win.

Repeat 12 times.

You wont be able to get zombie kill of the week playing solo. You will need at least another controller.

To get zombie kill of the week you must activate a crane or blow up a propane tank or a car. In the chapter 5 side mission there are both a crane and tanks and cars.

What I did was to go back on my already completed campaign and go to the side mission of chapter 5. I believe it is the quickest mission to do in the game as the map is very short.

Using the second controller, get near zombies and let them kill you. On your main controller quickly get through the level. Do this 12 times.

Nightmare Clown has a very good solution.
I started using level 3 for this achievement which might be helpful if you are having trouble with the hoards or exploding zombies in the Expiration date bonus level.

Level 3 is very linear and can be rushed through in under 3 minutes. At the start of the level follow the path and shoot the red car causing it to explode and most likely kill a few zombies earning you your ZKOTW.
open the door to the store on the left side of the building and the upper chest should have a automatic weapon, head inside and follow the very linear path to the T-800s. I used Witchita's power in the middle of the T-800s and shot the decoy when it exploded it killed them, grab the key open the door and get the package.