Simply kill a zombie of any kind and by any means to get credit towards this achievement.
If you're looking to grind and help the community reach the total I suggest selecting higher levels of Breakdown as I believe more zombies spawn.
For those new to community challenges if we do manage to reach the goal for the achievement, it won't unlock till a couple days after the completion time.
In this thread Undead Labs community manager 'Undead Nicole' updates us on the totals for the challenges:https://forums.undeadlabs.com/threads/upcoming-monthly-chall...Edit
: You should have it unlocked on your profile if you played.