There are 12 Trophies that can be collected.

Bronze

3, 2, 1, GO!!
Complete your first Quick Race.

Game Gears
Complete Championship with manual transmission.

Long medium left … maybe
Play fifty games in any mode.

Conditioned Reflex
Win a Classic race five times.

Over Jump
Beat all five default ghost cars in Time Attack.

Go, Go, Sega Rally!
Win five online races.

Super Challenge
Unlock all courses.

Silver

Reckless Running
Touch all five AI cars before winning a Quick Race.

Ignition
Win a race with every car in the game.

Lakeside Memory
Finish 1st on Lakeside in Championship.

Finish!!
Place 1st on all tracks in Quick Race on Arcade difficulty.

Gold

Game Over, Yeah!
Unlock all cars and courses.

http://www.ps3trophies.com/forums/trophy-news/62006-sega-rally-online-arcade-trophy-list.html