The wording on this achievement thew me at first but all you need to do is hit or tap 20 enemies with a car. You'll gain access to vehicles once you've got out of Vavilov and enter the open world. I found my first car just after opening the gates and heading towards Lesnaya Station - parked on the roadside.
Interact with the car door to get in. Then floor it up and down the road until you kill or hit 20 enemies. On easy difficulty you can easily hit 30 or more before the car blows up!