Here is the full list of all 38 Skylanders: Spyro's Adventure trophies - there are 21 bronze, 12 silver, 4 gold and 1 platinum.
Unlock all other trophies.
The first time you put your Skylander on the Portal of Power.
Complete the Shattered Island level.
Complete the Stormy Stronghold level and acquire the elemental source.
Complete the Leviathan Lagoon level and acquire the elemental source.
Complete the Stone Town level and acquire the elemental source.
Complete the Falling Forest level and acquire the elemental source.
Complete the Battlefield level and acquire the elemental source.
Complete the Creepy Citadel level and acquire the elemental source.
Complete the Lava Lakes Railway level and acquire the elemental source.
Complete the Arkeyan Armory level and acquire the elemental source.
Complete the adventure mode by finishing the game.
Get 3 stars in any one level.
In the Leviathan Lagoon level, dodge 30 sharks without being hit.
In the Falling Forest level, defeat Evil Ent while more than 5 of Evil Ent's seeds are on the field.
Defeat Kaos' Evil minions in the Lava Lakes Railway level with only Gill Grunt's Power Hose.
Avoid being hit by the laser traps during the boss fight in the Creepy Citadel level.
Defeat Kaos without swapping Skylanders during the battle.
Defeat 30 enemies while riding the War Machine in the Arkeyan Armory level.
Never use any rocket in the Falling Forest level.
Get swallowed by the Leviathan 5 times in the Leviathan Lagoon level.
Destroy all of the rocks in the Molekin Mine level.
Complete the Troll Warehouse level without getting injured by the landmines.
Complete the Crystal Eye Castle level without being hit by any of the rolling barrels.
Complete your first challenge level!
Complete 3 Challenge levels.
The first time you purchase an upgrade for your Skylander.
Purchase all upgrades for any one Skylander.
Level up any one Skylander to level 10.
Collect 10 Hats.
Have your Skylander equip a hat for the first time.
Unlock any Elemental Gate.
Defeat 15 Chompies in the Shattered Island level.
Open any treasure chest.
Collect 10 Story Scrolls.
Collect 10 Legendary Treasures.
Collect 10 Soul Gems.
Play and complete any PvP match: win or lose.