To get this achievment, follow these steps:

1st - Take your car to the start of the track on Desert Island and wait for the racer to talk with you (If he doesn't, you're probably not well positioned)

2nd - After the dialoge, drive just a little bit forward, to be roughly at his side and wait until his engine starts

3rd - Drive close to the edges you'll need to turn - the racer will be faster than you, so this will help you to keep close distance

Final tip: be careful as to not be too close or to take a lead - winning the race or bumping into his car will end the challenge and you'll need to start over

Hope I could help! ❤