Play through any championship until you are challenged for the first special race(every 3 races), make sure you save at the prompt screen after you accept the challenge. Now start the special race and simply power off your Xbox. When you power up again that special race will be available in the championship challenge. If you continue the normal Championship you'll do race 3 again, then it'll offer you a different special race, save again, start and power off like before for another special race in Challenge mode. You can keep doing this until all are unlocked.