To unlock the Get A Little Blood on the Tires in Borderlands: Game of the Year Edition, you will need to kill a total of 25 enemies by running them over in your vehicle.
You will first have to progress far enough into the story that you gain access to the Catch-A-Ride station by completing the Bone Head's Theft quest. Once you have a vehicle, target low-level bandits and Skags and run them over. Once you have killed a total of 25 enemies the trophy will unlock.