Here is the full list of all 37 Spyro the Dragon trophies - there are 16 bronze, 17 silver, 3 gold and 1 platinum.
Collect all Spyro the Dragon Trophies
Collect all gems in Gnasty's Loot
Unlock Gnasty's Loot
Complete Icy Flight without touching the ground
Complete Wild Flight without touching the ground
Flame all Fairies in Crystal Flight
Flame all Fairies in Night Flight
Get Gnasty Gnorc to complete 5 laps
Destroy 6 gears in Twilight Harbor
Complete Gnorc Cove without killing any Rats
Defeat 4 Nightmare Beasts in one glide
Defeat all Tin Soldiers
Charge through 4 Puffer Birds in a row
Defeat 3 Demon Dogs in large form
Charge through 3 Armored Fools in a row
Collect 500 gems in Metalhead
Jump off every Supercharge ramp in Tree Tops
Free a trapped Chicken
Light 3 fireworks within 15 seconds
Flame 5 Glowing Mushrooms in Beast Makers
Collect 400 gems in Blowhard
Defeat hidden Egg Thief in Wizard Peak
Defeat all Metalback Spiders
Detonate 3 explosive chests on the pillars in Alpine Ridge
Charge through 4 Armored Druids near the start of Magic Crafters
Unlock the strong chest in Doctor Shemp
Defeat all three Ski Gnorcs
Flame every Vulture in Cliff Town
Charge a Vulture
Use a cannon to dispatch a taunting Gnorc
Do a loop around an arch
Defeat Toasty without getting hit by him
Glide to secret Egg Thief area in Town Square
Light the two bonfires in Dark Hollow
Find the hidden entrance to Sunny Flight
Take a trip with a Balloonist
Flame 10 sheep in Stone Hill