Just make sure that you don't come into contact with any other vehicles, signs on the side of track, walls, etc and you'll be fine with this achievement. Your finishing position in the race doesn't matter, as long as you don't hit anything. If you want to be totally safe, just take your time and finish the race in last place to ensure that all other drivers have a large enough lead that you don't have to worry about hitting them. Once the race is complete, you'll get this achievement.