Get in a car you like. Then open the menu and go to the Rivals tab. Select Festival Route Rivals. Find a race you like. Go to whichever class your car is in, but don't select it. Hit Y to Change Rival. Then either find somebody slower than you and beat their time or find somebody with a 'dirty' lap (it will have a yellow exclamation point beside it) and complete the race without hitting anything.
Selecting your rival makes this a lot easier than it may seem.