Here is the full list of all 105 Spyro Reignited Trilogy achievements. It takes around 30-35 hours to unlock all of the achievements on Windows.
Harbor Speedway: Find Hunter
Honey Speedway: Fly through 12 star speed boosts in one race
Frozen Altars: Use ice breath to freeze 12 enemies
Country Speedway: Fire 5 missiles in one race
Cloud Spires: Glide for 5+ seconds (and land safely!)
Defeat all Draclets in one Superflight
Defeat every Robo Bee by spitting
Defeat the Ox without taking a hit
Don't hit any Sheep in Cloud Temples
Charge through every Monkey in Mystic Marsh
Complete Gulp's Overlook without harming fodder
Don't get hit by Bob
Unlock the permanent Super Flame
Defeat the Snowmobiles before defeating a Hang Glider
Heat up the audience
Charge a Goat in Colossus
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
Clean run in the trolley
Flame the Pigeons first in Metro Speedway
Defeat every Earthshaper in Fracture Hills
Bugbot Factory: As Sparx, defeat the Metapede
Starfish Reef: As Sparx, defeat the Manta Ray
Enchanted Towers: Destroy all the balloons
Mushroom Speedway: Fly Through 4 Star Speed Boosts In One Lap
Fireworks Factory: Defeat Twin Dragons (Boss)
Haunted Tomb: Destroy All Sarcophagi
Crystal Islands: Defeat all the Crystal Bears
Dino Mines: As Agent 9, defeat an enemy with a ricochet shot
Desert Ruins: Find both butterfly jars
Midnight Mountain: Get revenge on Moneybags
Sorceress's Lair: Defeat The Sorceress
Lost Fleet: Use cannons to shoot down all vultures
Bamboo Terrace: Follow the question mark bottles to the end
Agent 9's Lab: As Agent 9, shoot down all the balloons
Midnight Mountain: Free Agent 9
Spider Town: As Sparx, defeat the Spider King
Crawdad Farm: Defeat the Crawdad King
Seashell Shore: Defeat Bluto's nuclear shark submarine
Scorch's Pit: Defeat Scorch
Evening Lake: Launch the Transporter Rocket
Charmed Ridge: Defeat a giant
Molten Crater: Unlock the locked treasure chest
Bentley's Outpost: As Bentley, destroy all the totem poles
Evening Lake: Free Bentley the Yeti
Spike's Arena: Defeat Spike
Midday Gardens: Launch the Transporter Whirligig
Sgt. Byrd's Base: As Sgt. Byrd, bomb all treasure chests
Midday Gardens: Free Sgt. James Byrd
Sheila's Alp: As Sheila, destroy all headbash treasure chests
Spooky Swamp: Defeat Sleepyhead
Icy Peak: Destroy 6 icy things using the cannons
Buzz's Dungeon: Defeat Buzz
Sunrise Spring: Launch the Transporter Balloon
Sunrise Spring: Free Sheila the Kangaroo
Sunny Villa: Defeat all Coward Rhynocs
Defeat 5 Buggies while charging
Headbutt every turtle in Turtle Soup challenges
Steal a Popcorn Crystal from Hunter
Use all 3 types of power-ups in Ripto's Arena
Use a cannon to defeat a TNT thrower
Headbash every rock in Winter Tundra
Complete the long glide to Orb in Autumn Plains
Destroy every Roboshark
Defeat every robot in Hurricos
Don't touch the hazardous water in Shady Oasis
Do not feed the Hungry Idol any red fish
Don't touch the lava in Skelos Badlands
Complete Crush's Dungeon without hitting any fodder
Complete Hunter's challenge
Light 6 Gem Lamps in 15 seconds
Destroy 6 gears in Twilight Harbor
Defeat all Tin Soldiers
Light 3 fireworks within 15 seconds
Do a loop around an arch
Jump off every Supercharge ramp in Tree Tops
Defeat hidden Egg Thief in Wizard Peak
Get Gnasty Gnorc to complete 5 laps
Charge through 4 Puffer Birds in a row
Flame 5 Glowing Mushrooms in Beast Makers
Free a trapped Chicken
Detonate 3 explosive chests on the pillars in Alpine Ridge
Complete Gnorc Cove without killing any Rats
Defeat 4 Nightmare Beasts in one glide
Defeat 3 Demon Dogs in large form
Charge through 3 Armored Fools in a row
Collect 500 gems in Metalhead
Defeat all three Ski Gnorcs
Flame every Vulture in Cliff Town
Flame 10 sheep in Stone Hill
Collect 400 gems in Blowhard
Defeat all Metalback Spiders
Charge through 4 Armored Druids near the start of Magic Crafters
Unlock the strong chest in Doctor Shemp
Charge a Vulture
Use a cannon to dispatch a taunting Gnorc
Take a trip with a Balloonist
Light the two bonfires in Dark Hollow
Defeat Toasty without getting hit by him
Glide to secret Egg Thief area in Town Square
Find the hidden entrance to Sunny Flight