Here is the full list of all 41 Spyro 3: Year of the Dragon trophies - there are 27 bronze, 9 silver, 4 gold and 1 platinum.
Win all trophies in Spyro 3
Midnight Mountain: Get revenge on Moneybags
Bugbot Factory: As Sparx, defeat the Metapede
Sorceress's Lair: Defeat The Sorceress
Dino Mines: As Agent 9, defeat an enemy with a ricochet shot
Harbor Speedway: Find Hunter
Desert Ruins: Find both butterfly jars
Haunted Tomb: Destroy All Sarcophagi
Crystal Islands: Defeat all the Crystal Bears
Starfish Reef: As Sparx, defeat the Manta Ray
Spider Town: As Sparx, defeat the Spider King
Crawdad Farm: Defeat the Crawdad King
Agent 9's Lab: As Agent 9, shoot down all the balloons
Midnight Mountain: Free Agent 9
Scorch's Pit: Defeat Scorch
Evening Lake: Launch the Transporter Rocket
Charmed Ridge: Defeat a giant
Honey Speedway: Fly through 12 star speed boosts in one race
Lost Fleet: Use cannons to shoot down all vultures
Frozen Altars: Use ice breath to freeze 12 enemies
Bentley's Outpost: As Bentley, destroy all the totem poles
Evening Lake: Free Bentley the Yeti
Fireworks Factory: Defeat Twin Dragons (Boss)
Spike's Arena: Defeat Spike
Midday Gardens: Launch the Transporter Whirligig
Bamboo Terrace: Follow the question mark bottles to the end
Country Speedway: Fire 5 missiles in one race
Enchanted Towers: Destroy all the balloons
Icy Peak: Destroy 6 icy things using the cannons
Sgt. Byrd's Base: As Sgt. Byrd, bomb all treasure chests
Spooky Swamp: Defeat Sleepyhead
Midday Gardens: Free Sgt. James Byrd
Buzz's Dungeon: Defeat Buzz
Sunrise Spring: Launch the Transporter Balloon
Molten Crater: Unlock the locked treasure chest
Mushroom Speedway: Fly Through 4 Star Speed Boosts In One Lap
Seashell Shore: Defeat Bluto's nuclear shark submarine
Cloud Spires: Glide for 5+ seconds (and land safely!)
Sheila's Alp: As Sheila, destroy all headbash treasure chests
Sunny Villa: Defeat all Coward Rhynocs
Sunrise Spring: Free Sheila the Kangaroo