There are 12 Trophies that can be collected.

Bronze

Race Apprentice
Win your first race.

Newcomer
Win your first online ranked match.

'Normal' Champion
Beat all Normal Challenges.

'Fast' Champion
Beat all Fast Challenges.

Shadow Takedown
Pull out one opponent with the Speed Disruptor in Shadow Mode.

Score Seeker
Score at least 15000 points in Turbo Challenge #13.

Wrong Direction
Complete a lap on Peak in 18.1s – driving in the wrong direction, multiplayer only.

Silver

Homerun
Win 3 online ranked matches in a row.

Globetrotter
Win an online match on each track of the base game (forwards and backwards).

'Turbo' Champion
Beat all Turbo Challenges.

Destructoid
Waste 100 opponent vehicles with weapons in any mode.

Gold

Motorhead
Unlock all Tracks, Vehicles and Race Classes.

http://www.ps3trophies.org/game/tnt-racers/trophies/