There are 38 Trophies that can be collected.

Bronze

Hello Skylander!!
The first time you put your Skylander on the Portal of Power.

Home Sweet Home
Complete the Shattered Island level.

Fresh Air
Complete the Stormy Stronghold level and acquire the elemental source.

Pure Water
Complete the Leviathan Lagoon level and acquire the elemental source.

Mother Earth
Complete the Stone Town level and acquire the elemental source.

Light of Life
Complete the Falling Forest level and acquire the elemental source.

Perfect Technology
Complete the Battlefield level and acquire the elemental source.

Undead Spirit
Complete the Creepy Citadel level and acquire the elemental source.

Dancing Fire
Complete the Lava Lakes Railway level and acquire the elemental source.

Phew! That was close!
In the Leviathan Lagoon level, dodge 30 sharks without being hit.

Dodge Ball
In the Falling Forest level, defeat Evil Ent while more than 5 of Evil Ent's seeds are on the field.

Tag me if you can!
Avoid being hit by the laser traps during the boss fight in the Creepy Citadel level.

No Rocket Fired!
Never use any rocket in the Falling Forest level.

Leviathan Dentist
Get swallowed by the Leviathan 5 times in the Leviathan Lagoon level.

I love smashing!
Destroy all of the rocks in the Molekin Mine level.

New Challenger
Complete your first challenge level!

I love shopping
The first time you purchase an upgrade for your Skylander.

Fashion Stylist
Have your Skylander equip a hat for the first time.

Inside Power
Unlock any Elemental Gate.

Happy Hour
Open any treasure chest.

The First Battle
Play and complete any PvP match: win or lose.

Silver

Magic Time
Complete the Arkeyan Armory level and acquire the elemental source.

Call Me Fireman!
Defeat Kaos' Evil minions in the Lava Lakes Railway level with only Gill Grunt's Power Hose.

The Ace Pilot
Defeat 30 enemies while riding the War Machine in the Arkeyan Armory level.

Mine Detector
Complete the Troll Warehouse level without getting injured by the landmines.

Get me if you can!
Complete the Crystal Eye Castle level without being hit by any of the rolling barrels.

Can't stop me!
Complete 3 Challenge levels.

Gotta buy them all
Purchase all upgrades for any one Skylander.

Fashion Elite
Collect 10 Hats.

Chompy Chopper
Defeat 15 Chompies in the Shattered Island level.

Archaeologist
Collect 10 Story Scrolls.

Treasure-hunter
Collect 10 Legendary Treasures.

The Spiritual Mentor
Collect 10 Soul Gems.

Gold

The Savior
Complete the adventure mode by finishing the game.

Star Chaser
Get 3 stars in any one level.

One for All!
Defeat Kaos without swapping Skylanders during the battle.

Climb to the Top
Level up any one Skylander to level 10.

Platinum

True Portal Master
Unlock all other trophies.

http://www.ps3trophies.com/forums/ps3-trophy-news/2914-skylanders-spyros-adventure-trophy-list.html