This is a "monthly" rivals event. You will need the 1967 Brabham BT24, which is part of the Nürburgring Booster Car Pack (paid DLC). If you have the Car Pass you'll get it for free.
Good news is you can only enter the rivals event with the stock version of the car, so no tuning necessary! The track is Bugatti Circuit on Le Mans, which is 4.273 km (2.655 mi) long. Expect to take about 15 or 20 minutes to earn the challenge.
Simply enter the event, complete one lap, and then press start and select "Finish Race" (there's no need to beat a rival or get a specific time). After the post-race screens with the exp and credits earned hit restart (so you don't have to go through the menu loading screens). Do the event like this 5 times total and your achievement will pop at the end of the fifth.