When presented with the pre-race screen where you can change difficulty and view competitiors, look above the menu options. The current race objective is shown here, complete it to get bonus reputation points.
The difficulty of the task set scales with the potential reward points, and is dependant on the liveries you race in. It tends to be finish within X time, reach V speed, or pass the finish line at Z speed. Complete 5 of these objectives to gain the achievement - not too difficult to do in the early campaign seasons.