In the Challenge Series menu complete the following events to unlock the corresponding car.

Unlock Mazda RX7 (Tuner):
In the Boss Battle beat Kenji.

Unlock Nissan 240SX (Tuner):
Complete ALL 3 'Checkpoint' challenges.

Unlock Aston Martin DB9 (Exotic):
In the Boss Battle beat Wolf.

Unlock Jaguar XK 2007 (Exotic):
Complete ALL 3 'Turf War' races.

Unlock Dodge Charger RT Classic (Muscle):
Beat the 21st Muscle Car Gang.