Go to "Autoshow" and "View All" Press "Y" and filter to "Classic Racers" then press "B" you then should have a list of cars you can choose from that you will need to complete this challenge.
Classic Racer Cars Alfa Romeo Giula TZ2 - 1965
Alfa Romeo 33 Stradale - 1968
Ferarri 250 Testa Rossa - 1957
Ferrari 500 Mondail - 1953
Ferrari 250 GTO - 1962
Ferrari 330 P4 - 1967
Ferarri 250LM - 1963
Fiat Dino 2.4 Coupe - 1969
Ford Lotus Cortina - 1966
Ford GT40 MK II - 1966
Jaguar D-Type - 1956
Maserati 300 S - 1957
Maserati Tipo 61 Birdcage - 1961
Mercedes-Benz 280 SL - 1967
Porsche 550 Spyder - 1955
Porsche 718 RS 60 - 1960
Shelby Cobra Daytona Coupe - 1965
Also available in the Barn Find section
Once you have chosen your car complete a Championship by driving or Fast travelling to a race destination and selecting Championship on the menu. Once Championship races have been completed then the challenge achievement should then pop.