This is actually really easy... when the race starts let everyone go past you and just keep your distance.
When you finish the race the achievement should pop.
Warning: Do not fall too far behind as if you don't finish within 30 seconds after the winner does, you will get a DNF and not get the achievement. Another thing you want to avoid is riding the horse too hard which will result in it kicking you off and the achievement to not unlock.
If it does not unlock when it is supposed to try returning to Free Roam, then re-entering another Grand Prix.