This may be cumulative, but I did this in one session....
To access Time Trial Mode, select Arcade from the main menu. After selecting your track and car (If you want to get this out of the way quickly then the shortest track is Mythic, Utah.) you then get to select your mode.
You will then need to race 6 laps. The first lap you will set a time and then the remaining 5 will be you racing against your ghost. The achievement will unlock as soon as you complete the 6th lap.