EDIT: Please note that some of you are reporting this achievement may be glitched. It may pop or not.
This achievement is easier than it may seem.
Select the Azure Circuit track in a Quick Race. The car you use does not matter, although try to select a car that is small. I personally set the race with 1 AI, 2 laps, and did it with a Formula Golf 1000. Make sure you have the race guideline on.
Once the green light drops, make a 180 turn and from here you have the option to do the lap only looking at your mirror or keeping the look back button pressed down (I set that button to
). Complete the lap without bumping into anyone or anything and the achievement is yours!
Here is a video example of how to do it: