From the main menu, select rivals. You have three different types, monthly, weekly and daily events to accumulate 300 points. They are hot laps (one lap time trial) or pacesetter (three lap time trials, average time counts) events.
You need 10 times in those events, so one monthly, which is active all season, one weekly, and then depending when you start either 8 more dailies or 7 dailies and one more weekly is enough for the achievement.
Make sure you are actually setting a time, so do not leave the track or your time will be invalid. On your way, depending on you your rank, you might also unlock