After defeating Amy in a 1v1 she calls offering a race with some pros. The track is once you go fast. In order to win you need to post the 1st or 2nd best lap time.
First make sure your horse power is at least 350 preferably 400. I strongly advise you to buy improved parts from the garage this can make a massive difference and is sometimes more effective then buying a new car.
The track is narrow with sharp turns. Set the handling of the car to grip and buy grip tyres. Having a small nimble car really helps as your speed drops really low due to the sharp turns and larger cars struggle to regain the momentum.
There is no set time to beat as is it dependent on the results. Try to learn the track rather then rely on the mini map. I used the Lotus Exige which was only a 45k car but the upgrades really supercharged this. I would say the biggest tip I can give other then using a smaller fast car and learning the track is to customise the handling and parts.