Need for Speed Payback

It will be very difficult to miss this through the course of the game.

Each race has a 'Beat this time' aspect to it, whether it being a time a friend of yours has set, or a general autolog suggestion if no one on your friends list has done that race. If you come in under the time posted, you'll unlock the achievement.

If you're really struggling, bring an upgraded car to a lower level race, and you should have an easy time.