Select "Single Race" from the main menu, then change from "Arcade" to "Drive or Explode". You can select any other options you'd like for length/track/driver/vehicle, this solution doesn't depend on anything.
When the race starts, simply slam on your brakes. You can wait until the timer slowly runs your health down, or Austin Powers' yourself in between the track barriers and reverse/accelerate to chip away your health bar. As long as you explode before you cross the first checkpoint, or have the other drivers trigger the TimeBomb, the achievement will pop almost immediately.