For this trophy you have to have driven each of the new Exotic cars in either an Online Race or an Online Time attack race.
The cars are as follows:
Alfa Romeo 8C Competizione
BMW M1 Procar
Honda (Acura in US) NSX
Maserati GranTurismo S
Mercedes-Benz SLR McLaren Stirling Moss
The fastest way you can do this is to either setup a ranked or unranked online race on Miyatomi as it takes roughly 20 seconds a lap and cycle through each car.