please let me add: I managed to unlock the Achievement at the Crossbay Tunnel (Basic Route #72) on the Straight at the end of the Race, and, I didn't get time to straighten up the car, so I ended up going over the Finish Line on an angle (405 Degrees Left (I Believe)).
So, therefore, you don't have to Straighten Up the Car to get the Achievement, also, I think you may have to come in 1st, but I could be wrong, because I got the Achievement when I came in 1st and won the Race.
Unfortunately, this Achievement can only be obtained through Story Mode (Doing Races in the Ridge Racer World Explorer, it cannot be obtained Online (Xbox LIVE) or in Split-Screen Racing (Offline).
For the YouTube Video: this is the best one I could find (after long time of Searching on YouTube for a Video for this Achievement), unfortunately, the View from the Car makes it harder to interpret how to do a 360 Degrees Flat Spin, but, as I said earlier, this is the best one I could find for this Achievement.
All credit in the YouTube Video goes to rick0708, this is not my Video.