Like with the first Beat The Team achievement, although this video shows you how to get the achievement with the ELITE GT12, I would suggest doing the same route with the COBRETTI 530 GTS. I found getting the achievement much easier with the COBRETTI.
With the COBRETTI, do not worry about hitting the walls and do not really try to avoid it. Just make sure that you are bouncing off of them, not sliding against them, and always hitting them with the side of the car and you should not crash. You also do not need to let up on the gas in the beginning to avoid drifting.
All credit for the video goes to the wonderful people at Achievement Hunter.