Drive a total of 1,000 miles in vehicles in "Jimmy's Vendetta."
You probably won't get this through normal playthrough of the DLC. On average you will only accumulate 200-300 miles per game. You can check your progress by opening the Game Statistics from the pause menu where it's listed under "Distance traveled by car."
The counter is carried over from one playthrough to the next, so you can either drive around until you reach 1000 miles or start a new game. It's best to leave this one for last as you will be adding miles to the counter as you complete all your other achievements.
There's a glitch in the game that will allow you to get this without having to drive the miles; however, it's a rather long process. See Millionaire for details.