There are 12 Trophies that can be collected.

Bronze

Overachiever
Be the winner or on the winning team who has reached the kill or flag limit before time's up in an online match.

In the Mode
Win an online match in each mode on every map.

Road Rambo
Be the first to kill an opponent as each class of car in online matches.

Thrillkiller
Kill three or more opponents within four seconds without dying on every map in every car in online matches.

Full-Timer
Play through one hundred online matches from start to finish.

Grabby, Grabby, Grabby!
Obtain every type of pickup at least once on every map in online matches.

Team Leader
Be the highest-scoring player of a winning team in 10 online team matches.

Silver

Perfect Double
Charge your shields up from zero to full in an online game by performing a perfect double somersault (720 degrees).

The Long Haul
Bring the opposing team's flag from their base to your team's base two hundred times in online matches.

Bloodlust
Be the first to kill an opponent in fifty online matches.

Nothing Can Kill Me!
Receive damage from every type of weapon without dying in an online match.

Gold

Unstoppable!
Survive an online match from start to finish without dying.

http://www.ps3trophies.com/forums/playstation-trophy-news/13666-wheels-destruction-world-tour-trophy-list.html