Hi, this isn't a real solution but maybe it helps you:
The 2.4 Hours of the Ring Event is available in the Hopper Menu. Every Race is a P-class event and takes 2 hours and 40 minutes (!).
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.
English isn't my mother tongue, so maybe there are some language mistakes.
EDIT: Some people said this challenge is harder to get than the other ones cause they had less time left when they reached 250 miles. So keep pushing and drive fast and clean.