Apparently remy is really useful character. From the main menu, select time trial rather than the regular mode. Your goal is to reach as many finish lines as possible within the time you have. There are blue orbs located around the map, which I believe give you extra time. (though don't worry to much about time, I in the end idled about 15 minutes just to finish the game. From my understanding, 10 passengers/finish lines reached will give you an A, though I'm not 100% sure. Requirements might be a bit lower, or have other factors included. Extra info is welcome if this in incorrect.
Edit: seems to be indeed 10 passengers for an A. Getting hit by a car will reset your progress. You can hit restart when you reach 10 passengers. (Thanks to shadow kisuragi)