You get this by going to your phone in game, then to the multiplayer option, then to bounty hunter, then to Find a Target. After this, someone in game will be running away from you and the police. Kill them and do it 4 more times.
To check your kills, go to the Xbox Achievements App and it's one of the tracked stats at the top of the page.
EDIT: If you've seen this solution before, it's being changed dramatically. Throughout the updates and the changes, it's clear that Ubisoft is allowing all forms of killing to be counted. So just murder away. I still recommend hacking their car to stop and then sniping them out of the drivers seat, but to each their own.
SECOND EDIT: It appears this now works via four-player private lobby as well. (Thanks xDaddy Cake)
Good luck!