The Walkers and Biters achievement in State of Decay 2 is pretty self-explanatory. You need to kill 1,000 zombies. This will come naturally if you play more than a few hours but if you really want to expedite the process, bring a car with plenty of gas and repair kits if you can find or make any. Driving around and hitting every zombie on the way, especially hordes, will most efficiently boost your kill count.
You can also stop for infestations and plague hearts you see on the way, as these both spawn plenty of zombies as well.