Beat the other racers and come in at least fourth place to earn a C-rank in ALL Street Showdown side missions. You unlock more Street Showdown side missions and Performance Upgrades on all player vehicles for a A-rank or better. There are 15 total.
TIP #1: If you Airjack to a Super Bike as soon as you can, it makes the races a lot easier and for the races where you start on a bike just use Aimed Shot or Cyclone to kill all your opponents. Try to take shortcuts whenever possible because the other cars tend to only follow the road. Additionally, use boost whenever you can.