To earn this trophy (and all the similar trophies that come before it), you must earn enough Speed Points to race the Most Wanted car. You must go head to head with it and win. After winning races against cars on the Most Wanted list, you don't win the car straight away, you must shut them down afterwards by chasing them and performing a take down, making them crash and earning yourself the new car.
It's possible for the Most Wanted cars to escape from you when you're trying to shut them down but don’t worry, they randomly speed past you again when you're driving around the city, showing up as a black arrow on the mini-map. This happens quite frequently so there are plenty of chances to shut them down.
You will require a total of 1,000,000 SP to unlock this event.