To get "Go the Distance", you need to win one of the four longer races in the main disciplines. To unlock those races, you have to get to specific levels in that respective series. The races, race series and unlocks are:
Dirt Racing - The Gaunlet - unlocks at level 8
Cross Country - The Titan - unlocks at level 8
Street Scene - The Marathon - unlocks at level 9
Road Racing - The Colossus - unlocks at level 10
If you want to get this out of the way fast, concentrate on racing dirt or cross country after you finished the 4 season introduction and gained access to the complete horizon lineup. However, these do not take too long to unlock even when spreading your races throughout different disciplines and you need to get to level 10 anyways for all the series-related achievements.
There are no car or class restrictions, so you can take your favorite or fastest car. The races are a bit longer than usual, it took me 10 minutes to finish The Gaunlet in an S850 Audi Sport Quattro.
edit: added the different levels to unlock the races.