I recommend choosing one of the Road Rage events in the northeast corner of the map, since there are two repair shops that are close together, one of which you should have revealed on your map right from the get-go.
Remember that nothing prevents you from pulling a U-turn in a Road Rage event, so knock yourself around until you get the Critical Damage warning onscreen. Ensure that you have been zipping back and forth around the same stretch of road to keep you close to the nearest repair shop so that it's easier to get back to it when you really need it.
Drive through the repair shop before time runs out on the event and the Achievement will unlock. You do not need to actually win the event to earn the Achievement.