Destroy 10 wanderers.
Wanderers are a type of car, the look similar to Army type hummers.
Destroy 50 sharks.
They look similar to Ford GT/Corvettes
Rival cars all have different names starting with Wanderers, Akaris, Nukems, Sharks and Classics. When you first start you will notice that all of the Red arrows driving around the city are akaris and the pink ones are classics. The two car related trophies require that you destroy the Sharks and wanders. Both of these can be found in various missions such as arena, theft etc. But the best mission to do this is Port: Guard. It's a side mission found in the Port area. Once available, play this; the only car that you have to destroy are sharks and wanderers. Other in game trophies require you to get other cars such as Nukem, Megrat etc. This is best done by going to mission select and choosing City>Testosterone. This is an arena match where you have to destroy 5 other vehicles to win. Just farm this for the vehicles you need and once finished press
to restart as your progress saves after every match rather than quitting and starting it back up. I advise doing this at the end when you have nothing else to do. If you want to know what a vehicle looks like go to your garage and look at the locked vehicles and their names; this will tell you what a Megrat, Shark, akari etc looks like etc.