First of all turn down the difficulty to easy. Immediately after the introduction in the game you have your first real race. This is the race we're going to use to get you the achievement. Why? Well, there are only 5 opponents and that's the least we'll encounter.
You'll start from fifth place. So the first thing to do is let the number 6 overtake you. Now the race is on. Start overtaking every opponent. Whenever you overtake one make sure you bump into the side of that car. That way you don't lose speed. Do this with every opponent.
Last thing to do is making sure you finish first. Since we turned down the difficulty this shouldn't prove too hard. As soon as you cross the finish line in first place the achievement will pop.