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.
Sorceress's Lair: Defeat The Sorceress
Honey Speedway: Fly through 12 star speed boosts in one race
Midnight Mountain: Free Agent 9
Desert Ruins: Find both butterfly jars
Crystal Islands: Defeat all the Crystal Bears
Scorch's Pit: Defeat Scorch
Evening Lake: Launch the Transporter Rocket
Bentley's Outpost: As Bentley, destroy all the totem poles
Evening Lake: Free Bentley the Yeti
Charmed Ridge: Defeat a giant
Frozen Altars: Use ice breath to freeze 12 enemies
Spike's Arena: Defeat Spike
Midday Gardens: Launch the Transporter Whirligig
Bamboo Terrace: Follow the question mark bottles to the end
Sgt. Byrd's Base: As Sgt. Byrd, bomb all treasure chests
Icy Peak: Destroy 6 icy things using the cannons
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
Sunny Villa: Defeat all Coward Rhynocs
Sunrise Spring: Free Sheila the Kangaroo
Use all 3 types of power-ups in Ripto's Arena
Headbutt every turtle in Turtle Soup challenges
Steal a Popcorn Crystal from Hunter
Defeat every Robo Bee by spitting
Complete Gulp's Overlook without harming fodder
Don't touch the hazardous water in Shady Oasis
Use a cannon to defeat a TNT thrower
Complete Crush's Dungeon without hitting any fodder
Defeat every robot in Hurricos
Complete Hunter's challenge
Light 6 Gem Lamps in 15 seconds
Take a trip with a Balloonist
Find the hidden entrance to Sunny Flight
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
Do not feed the Hungry Idol any red fish
Charge a Goat in Colossus
Destroy every Roboshark
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
Clean run in the trolley
Don't get hit by Bob
Defeat every Earthshaper in Fracture Hills
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 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
Sheila's Alp: As Sheila, destroy all headbash treasure chests
Mushroom Speedway: Fly Through 4 Star Speed Boosts In One Lap
Crawdad Farm: Defeat the Crawdad King
Enchanted Towers: Destroy all the balloons
Spooky Swamp: Defeat Sleepyhead
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
Fireworks Factory: Defeat Twin Dragons (Boss)
Starfish Reef: As Sparx, defeat the Manta Ray
Midnight Mountain: Get revenge on Moneybags
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
Bugbot Factory: As Sparx, defeat the Metapede