This achievement is for reaching REP Level 50.
You can do this a multitude of ways such as completing activities, winning races and outrunning the cops. Once you get your car over 350 PI, you should have access to all the races and bigger rewards. Most races should give you over 30,000-40,000 REP and you'll gain one heat level afterwards, so that rep you earned will be multiplied by your heat level.
The easiest way to do this, in my opinion, is to play through the game normally. Once you have a car that has over 350 PI, use the below method to easily rack up REP:
Just as a reference, the Huayra I'm using was over 400 PI at the time, but you don't need to 3 star every activity to earn rep. I did a big chunk of this REP gaining with a 300 PI Huracan.
Just keep doing this until you have a comfortable amount of REP you want to bank. Once you've banked enough to hit 50, you'll unlock your achievement.
This method is also great for earning the achievement for disabling 100 cops and evading 100 pursuits:
Going over the ramp shown further in the video (not the one with the activity over the yacht) will always wreck any cops chasing you, thus allowing you to escape.