There are 50 trophies that can be collected.

Bronze

The Start of Something Big
Complete a season on any Navigation Setting (Excluding Free Ride) (SP)

Ready to Ride
CaReady to Ridelibrate the board

Eager Student
Tricktionary: Visit the Tricktionary for the first time

Adept Skater
Tricktionary: Perform every non-Signature Skate Trick at least once (SP)

Adept Boarder
Tricktionary: Perform every non-Signature Snowboarding Trick at least once (SP)

See You In Indianapolis!
Tricktionary: Perform 500 Ollies (SP)

Making Hamburger
Tricktionary: Grind at least 500 feet in every type of Grind (Parallel, Slide, Angled) (SP)

Grabby McGrab Grab
Tricktionary: Perform 250 total Grabs (SP)

Skateboard Master!
Training Mode: Complete every Lesson in Skate Training on the Casual Setting

Snowboard Master!
Training Mode: Complete every Lesson in Snow Training on the Casual Setting

Well Balanced Individual
Complete a session in Regular Stance & a session in Goofy Stance (without leaving game – SP)

Control Freak
Complete a session on each Navigation Setting (without leaving game – SP)

Get a Real Skateboard!
Challenge Mode: Complete 15 total Insane Challenges

Reality Star
Challenge Mode: Complete all Videographer Challenges

Bags Packed
Unlock a new level

Steering Sensation
Unlock all Navigation Settings

Oh, the Places You Will Go!
Unlock every level in the game

Now You're Just Bragging!
New Orleans: Scoring Spots: Perform the bonus task of all 5 Scoring Spots (SP)

Scared of Bubbles
Melbourne: Point Rush: Finish with a score of at least 75 without collecting any Point Bubbles (SP)

Shiver Me Timbers!
Morocco: Complete any session in Morocco as Seadog O' Banion (SP)

You Got HOW MANY Points?!
Wallows: Scoring Spots: Score 1,000,000 total points (SP)

Don't need no Stinkin' GRINDS!
Santorini Trick Mode: Score 100,000 points without using grinds (SP)

Great Wall Master
Acquire all 4 Stars on Beijing Big Air & all 4 Stars on Beijing Halfpipe

Groove Me Baby
Grind Pro Trial: Perform 10 Grind Transfers in a session on any Grind Pro Trial (SP)

Going Steady with 2 Wheels
Manual Pro Trial: Maintain a continuous Manual for 500 feet on any Manual Pro Trial (SP)

Atmospheric Rotation
Big Air Pro Trial: Perform two 360° Spins in the same Big Air Pro Trial session (SP)

House of Horrors
Survival Mode: Survive the Huckjam Park Combo Level

Multiple Tricksters
'Challenging' High Wire Act

Bubbles Bubbles Everywhere…
Online Mode: Win a Point Rush session

King of the Hill
Online Mode: Win a Scoring Spots session

Silver

Jambalayanism
New Orleans: Acquire all 16 Stars

Down Under Daredevil
Melbourne: Acquire all 16 Stars

Mediterranean Maestro
Morocco: Acquire all 16 Stars

Hawaiian Hooligan
Wallows: Acquire all 16 Stars

Meeting of the Minds
Santorini: Acquire all 16 Stars

Whistle Blower
Whistler Mountain: Acquire all 16 Stars

4 Étoiles sur la Montagne
French Alps: Acquire all 16 Stars

Some Kind of Funhouse!
Huckjam Park: Acquire all 12 Stars on any Huckjam Park level

Tony Would Be Proud
Acquire all Stars in the Skateboard Tier on any Naviation Setting

Powder Prowess
Acquire all Stars in the Snowboard Tier on any Navigation Setting

The New Pro
Acquire all Stars in the Pro Trial Tier on any Navigation Setting

Gold

Serious Playtime
Complete each session type in each level on any Navigation Setting (Excluding Free Ride) (SP)

All-In-1 Shredder
Acquire all Stars in the Game on any Navigation setting

Platinum

Platinum
Unlock all other trophies

5 Secret

http://www.ps3trophies.org/game/tony-hawk-shred/trophies/