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