Hi, this isn't a real solution but maybe it helps you:
The 2.4 Hour D'Endurance Event is available in the Hopper Menu. Every Race is a 2-class event and takes 2 hours and 40 minutes (!). Its totally random if you get a R-class or a P-class car. In a P-class car it's easier to reach the 250 miles / 402 km but in the R-class its also easy to do.
You have to finish the race to get the achievement, don't leave the race before it ends, even if you reached the 250 miles / 402 km.
The hardest part is to find a race, cause every event takes 2 h 40 min. I would suggest searching after lobbys until you find one where the race ends in 30 minutes or less. Stay in the lobby and wait till the others finish their race and you can start. Sometimes you will be lucky enough to enter a lobby thats only a few seconds before the start of the race, but most people wont have this luck.
Attention: This race is set to simulation so you can get damage and you need to make a pitstop cause otherwise you will ran out of fuel.
English isn't my mother tongue, so maybe there are some language mistakes.
Here is a picture of my lobby, you can see everybody was able to get the challenge.