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