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)
Bugbot Factory: As Sparx, defeat the Metapede
Midnight Mountain: Get revenge on Moneybags
Sorceress's Lair: Defeat The Sorceress
Dino Mines: As Agent 9, defeat an enemy with a ricochet shot
Harbor Speedway: Find Hunter
Haunted Tomb: Destroy All Sarcophagi
Enchanted Towers: Destroy all the balloons
Desert Ruins: Find both butterfly jars
Starfish Reef: As Sparx, defeat the Manta Ray
Spider Town: As Sparx, defeat the Spider King
Crawdad Farm: Defeat the Crawdad King
Seashell Shore: Defeat Bluto's nuclear shark submarine
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
Honey Speedway: Fly through 12 star speed boosts in one race
Charmed Ridge: Defeat a giant
Bentley's Outpost: As Bentley, destroy all the totem poles
Evening Lake: Free Bentley the Yeti
Frozen Altars: Use ice breath to freeze 12 enemies
Lost Fleet: Use cannons to shoot down all vultures
Spike's Arena: Defeat Spike
Midday Gardens: Launch the Transporter Whirligig
Bamboo Terrace: Follow the question mark bottles to the end
Spooky Swamp: Defeat Sleepyhead
Country Speedway: Fire 5 missiles in one race
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
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
Cloud Spires: Glide for 5+ seconds (and land safely!)
Sunny Villa: Defeat all Coward Rhynocs
Sunrise Spring: Free Sheila the Kangaroo
Unlock the permanent Super Flame
Don't hit any Sheep in Cloud Temples
Defeat the Ox without taking a hit
Flame the Pigeons first in Metro Speedway
Defeat 5 Buggies while charging
Defeat the Snowmobiles before defeating a Hang Glider
Heat up the audience
Headbutt every turtle in Turtle Soup challenges
Do not feed the Hungry Idol any red fish
Don't get hit by Bob
Use all 3 types of power-ups in Ripto's Arena
Defeat every Robo Bee by spitting
Charge through every Monkey in Mystic Marsh
Headbash every rock in Winter Tundra
Defeat all Draclets in one Superflight
Complete the long glide to Orb in Autumn Plains
Complete Gulp's Overlook without harming fodder
Don't touch the lava in Skelos Badlands
Defeat every Earthshaper in Fracture Hills
Steal a Popcorn Crystal from Hunter
Don't touch the hazardous water in Shady Oasis
Clean run in the trolley
Use a cannon to defeat a TNT thrower
Complete Crush's Dungeon without hitting any fodder
Defeat every robot in Hurricos
Charge a Goat in Colossus
Destroy every Roboshark
Complete Hunter's challenge
Light 6 Gem Lamps in 15 seconds
Do a loop around an arch
Collect all gems in Gnasty's Loot
Unlock Gnasty's Loot
Defeat 4 Nightmare Beasts in one glide
Complete Icy Flight without touching the ground
Charge through 4 Puffer Birds in a row
Defeat 3 Demon Dogs in large form
Defeat all Tin Soldiers
Charge through 3 Armored Fools in a row
Complete Wild Flight without touching the ground
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
Use a cannon to dispatch a taunting Gnorc
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
Charge a Vulture
Light the two bonfires in Dark Hollow
Defeat Toasty without getting hit by him
Flame 10 sheep in Stone Hill
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
Take a trip with a Balloonist
Find the hidden entrance to Sunny Flight
Glide to secret Egg Thief area in Town Square