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.
Enchanted Towers: Destroy all the balloons
Icy Peak: Destroy 6 icy things using the cannons
Crawdad Farm: Defeat the Crawdad King
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
Mushroom Speedway: Fly Through 4 Star Speed Boosts In One Lap
Headbash every rock in Winter Tundra
Complete Gulp's Overlook without harming fodder
Defeat the Snowmobiles before defeating a Hang Glider
Steal a Popcorn Crystal from Hunter
Defeat every Earthshaper in Fracture Hills
Clean run in the trolley
Collect all gems in Gnasty's Loot
Unlock Gnasty's Loot
Defeat all Tin Soldiers
Get Gnasty Gnorc to complete 5 laps
Defeat 3 Demon Dogs in large form
Charge through 3 Armored Fools in a row
Collect 500 gems in Metalhead
Free a trapped Chicken
Complete Wild Flight without touching the ground
Collect 400 gems in Blowhard
Defeat hidden Egg Thief in Wizard Peak
Flame all Fairies in Crystal Flight
Defeat all Metalback Spiders
Seashell Shore: Defeat Bluto's nuclear shark submarine
Molten Crater: Unlock the locked treasure chest
Sunny Villa: Defeat all Coward Rhynocs
Complete the long glide to Orb in Autumn Plains
Complete Crush's Dungeon without hitting any fodder
Destroy every Roboshark
Heat up the audience
Defeat every robot in Hurricos
Headbutt every turtle in Turtle Soup challenges
Do not feed the Hungry Idol any red fish
Sheila's Alp: As Sheila, destroy all headbash treasure chests
Sunrise Spring: Free Sheila the Kangaroo
Charge a Goat in Colossus
Complete Hunter's challenge
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
Defeat Toasty without getting hit by him
Light the two bonfires in Dark Hollow
Glide to secret Egg Thief area in Town Square
Flame 10 sheep in Stone Hill
Find the hidden entrance to Sunny Flight
Do a loop around an arch
Use a cannon to dispatch a taunting Gnorc
Charge a Vulture
Flame all Fairies in Night Flight
Flame 5 Glowing Mushrooms in Beast Makers
Light 3 fireworks within 15 seconds
Jump off every Supercharge ramp in Tree Tops
Charge through 4 Puffer Birds in a row
Complete Icy Flight without touching the ground
Defeat 4 Nightmare Beasts in one glide
Complete Gnorc Cove without killing any Rats
Destroy 6 gears in Twilight Harbor
Light 6 Gem Lamps in 15 seconds
Defeat all Draclets in one Superflight
Don't touch the lava in Skelos Badlands
Use a cannon to defeat a TNT thrower
Don't get hit by Bob
Don't touch the hazardous water in Shady Oasis
Flame the Pigeons first in Metro Speedway
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!)
Midday Gardens: Launch the Transporter Whirligig
Spooky Swamp: Defeat Sleepyhead
Bamboo Terrace: Follow the question mark bottles to the end
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