Shortly into 'The Caspian' mission you'll be tasked to locate the whereabouts of a vehicle (Bukhanka) that drove away from the train.
Following the mission path through natural story progression you'll acquire the keys to the vehicle that drove away from you and earn:
Now that you have the car you can start driving around the desert wastelands running things over as that's the only way you can get kills with the Bukhanka. Everything counts such as Mutants, Bandits etc.
Honestly you can do this in any way you want but what I did was,
As soon as I saw a group on mutants in the distance I paused the game and quick saved. Then ran over the mutants making the achievement progression go up. Then after they were all dead I paused and pressed quick load and ran over the same group of mutants again.
OneBgBdArtemis Mentions that you can not Manual save in Ranger Hardcore. So if you find yourself on this difficulty I would recommend just driving up and down the map running things over as you go. I found the safe house which is kind of like a broken down ship (Far left, middle) to be a good spot for mutants to spawn.
You'll only have access to this vehicle in this section of the game so I'd recommend just getting it knocked out