This achievement must be done on the Race Track destination which you can travel to using the map.
There are plenty of cars that have the engine power to finish this track in time, however the real challenge is handling your vehicle as you navigate the turns.
I strongly recommend using an Xbox or equivalent controller for this achievement if you are playing on PC. The reason for this is because keyboard driving uses the W & S keys for acceleration and braking, the L & R triggers of a controller on the other hand are obviously more suited for controlling a vehicle, not to mention the smoother turning of a thumbstick. Make sure you aren't putting the acceleration trigger all the way down, you should be easing the trigger halfway down until it's safe to go top speed.
I was able to unlock this achievement with a DC Typhoon with a V8 OHV Supercharged engine, I think I had 26% improved tuning through parts (which was overkill), but the real trick is to combine racing slicks with race tires so you can stay on the track easier during straights. I put 2 vintage race tires up front and 2 slicks on the rear.
At that point it's a matter of learning the track. Figure out the turns, the straights, when to slow down and when to floor it and you'll have your achievement in no time.
Lastly, in case you didn't discover it on your own you can change the camera to be from the driver seat or a 3rd person angle, depending on your preference.