we have completed the challenge with 152 million zombie kills. it should unlock if you start up the game or if you are playing another game.
probably the best way to kill a bunch of zombies is to go to lifeline dlc and kill a bunch in the dead zones or just keep doing circles of the map and look for hordes.
Thanks to Dexter XBA you can check the progress here:
https://forums.undeadlabs.com/threads/community-challenge.49...