This achievement seems to only work in races with other cars (rally) - cannot complete in time attack, grinding, or crash events. You'll need to total/wreck your car BEFORE crossing the finish line, and then have the wreck skid across the line in 1st.
I recommend running a car that you have not leveled up the durability on, and then pick a race that has 4 or 5 laps (Class B or A). Run the race normally for the first several laps and try to build as large a lead as possible. In the last lap or so, start banging the car off the walls in an attempt to damage it. With a lower durability car, this won't take too much work (and you can maintain your lead). As you approach the finish line, your car should be just barely intact (flaming). Use nitro to slam the car into the wall at a low angle just before the finish line. If you had enough damage, you'll total the car and careen off the wall across the line for the win and achievement.