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