Hi, does anyone know how to unlock this car without cheats? Is it even possible?

It is possible, the easiest way to unlock it I believe is to win one of the championships but I am unsure as to which one you must win to unlock the car :/

I've earned all gold trophies in the game already and unlocked every other car, but this one is still missing for some reason. Challenge mode doesn't seem to unlock it too.

If that's the case then I can't really suggest anything else besides using the Unlock All Cars cheat which will unlock it for you, sorry :/