There are 45 trophies that can be collected.

Bronze

Ridiculously Long Lasting
Influence and reveal 5 gum company's billboards

It's Better Here
Influence and reveal all the restaurants

Mad Looks
Customize your character

Skate Guru
Convert 100 citizens

MannyMania
Manual for 75 meters in the story mode

Hoverboard
Grind 150 meters without touching the ground in the story mode

Fashionista
Collect 50 clothing items in the story mode

Raise the roof
Reach a trick height of 9 meters in the story mode

Riding Benefactor
Use 10 power ups on yourself or your team in one multiplayer match

Trip 'em up
Use 10 power ups to affect opponents in one multiplayer match

Infinite Arsenal
Use 12 power ups in one multiplayer match

Déjà vu?
Play each multiplayer mode once

Shape Master
Win a "Shaping Battle" multiplayer match

Dynamic Propaganda
Win a "Ministry vs Rising" multiplayer match

Unleash the Flow
Win a "Go with the flow" multiplayer match

Multiplayer Initiate
Complete a multiplayer match

Challenge Killer
Complete 35 challenges

Skatecopter
Perform 3 body rotations in a single trick

Shopping Spree
Unlock all the skate shops

Silver

Weapon of Mass Manipulation
Transform 1000 world objects and citizens

Secret Packrat
Discover all the secret challenges

Full Deck Trickster
Unlock all the tricks and complete your trick book

Speed Bomber
Obtain the best time in 3 time attack challenges

ApocalypsFlow
Reach 7500 flow in the story mode

Versatile Challenger
Win a match in every multiplayer game mode

Shaping Blitz
Shape 10 objects in one "Shaping Battle" multiplayer match

Absolute Truth
Convert 10 structures in a single "Ministry vs Rising" multiplayer match

Flow Factory
Obtain 8000 flow in one "Go with the flow" multiplayer match

Crossing the Beams
Link a shaping with a rail, or another shaping. Do this 30 times.

Flat footed
Perform 100 perfect landings

Glitterous
Find all the secret chests

Gold

Gold Medal Challenge
Earn the gold medal in all Shaun White challenges

Platinum

Platinum Award
Acquire all other trophies.

12 Secret

http://www.ps3trophies.com/forums/trophy-news/45945-shaun-white-skateboarding-trophy-list.html