DUE TO ROCKSTAR SHUTTING SERVERS DOWN, THIS TROPHY IS NO LONGER AVAILABLE!
This trophy is going to take a lot of patience to complete. Your system is going to freeze a lot and you will be hearing double beeps a lot.
Under the Modes section, there is an option to go Online. In this menu, there is the option to go into Rate My Ride mode. This is the mode that you are looking for.
This is the way that I did this to pop the trophy:
I rated one car then exited the mode completely.
I reversed into the garage and then exited to trigger a save.
When you finish rating a car and move onto the next, it DOES NOT save the rate to your count. If your system freezes at the point, kiss those rates goodbye.
Once again, this is very time-consuming because of the freeze. Good luck and have something else to do nearby.