There are 44 Trophies that can be collected.

Bronze

Welcome to Monster Jam!
Pass the test event

Bling
Equip an accessory on a monster truck

Speed Demon
Win a gold medal in 1 Circuit Racing event

Piston Popper
Win a gold medal in 1 Stadium Racing event

Crowd Pleaser
Win a gold medal in 1 Freestyle event

Time is on my side
Win a gold medal in 1 Time Crunch event

Shake and Bake
Win a gold medal in 1 Team Racing event

Gate Crusher
Win a gold medal in 1 Gate Rush event

Fast Learner
Win a gold medal in 1 Stunt Challenge event

Gearhead
Customize more than 5 monster trucks

Training Wheels
Reach level 5

Gas tank is half full
Reach level 10

Heartbreak Hill
Reach level 15

Beastmaster
Reach level 20

Sweep
Win a gold medal in 3 events in a row

Defy Authority
Defeat any two champion monster trucks in their home event

Can't be Stopped!
Perform 200 Big Saves in total

Tough
Win a gold medal in 5 different events on hard difficulty

I don't get Dizzy
Perform 100 Donut or Cyclone stunts in total

I think I'm gonna be sick
Perform 50 Flat Spin or Barrel Roll stunts in total

Showoff
Perform 50 Wheelie, Slap Wheelie or Stoppie stunts in total

Impossible!
Perform 25 Front or Back Flip stunts in total

Port of Call
Win a gold medal in at least 1 event in each stadium

Be your own Boss
Win a gold medal in every event of 1 stadium

Monster Mash
Destroy 250 obstacles in the game

You're the best around!
Win a gold medal in 20 events

Advance Auto Parts Upgrade
Unlock all Advance Auto Parts performace upgrades

Silver

Path of Destruction
Destroy 500 obstacles in the game

Veteran Driver
Earn 9,000 xp in a single event

Pro Driver
Win gold medals in 20 different events on hard difficulty

Freestyle Domination!
Win a gold medal in 1 Freestyle event with a score higher than 40

United Champion
Win both the Southern and Western National Tour

King of the Monsters
Defeat all 8 champion monster trucks once in their home event

Gold

World Finals Champion
Win all National Tours

Monster Jam Master
Win a gold medal in all events

Platinum

Grand Slam
Unlock all other trophies

8 Secret

http://www.ps3trophies.org/game/monster-jam-path-of-destruction/trophies/