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.
Spider Town: As Sparx, defeat the Spider King
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
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
Seashell Shore: Defeat Bluto's nuclear shark submarine
Molten Crater: Unlock the locked treasure chest
Cloud Spires: Glide for 5+ seconds (and land safely!)
Sheila's Alp: As Sheila, destroy all headbash treasure chests
Sunrise Spring: Free Sheila the Kangaroo
Sunny Villa: Defeat all Coward Rhynocs
Complete Crush's Dungeon without hitting any fodder
Unlock the permanent Super Flame
Defeat the Ox without taking a hit
Defeat 5 Buggies while charging
Headbash every rock in Winter Tundra
Use all 3 types of power-ups in Ripto's Arena
Complete Gulp's Overlook without harming fodder
Clean run in the trolley
Complete the long glide to Orb in Autumn Plains
Defeat the Snowmobiles before defeating a Hang Glider
Steal a Popcorn Crystal from Hunter
Defeat all Draclets in one Superflight
Use a cannon to defeat a TNT thrower
Destroy every Roboshark
Defeat every robot in Hurricos
Heat up the audience
Complete Hunter's challenge
Light 6 Gem Lamps in 15 seconds
Collect all gems in Gnasty's Loot
Unlock Gnasty's Loot
Defeat 4 Nightmare Beasts in one glide
Defeat Toasty without getting hit by him
Charge through 3 Armored Fools in a row
Charge through 4 Puffer Birds in a row
Defeat 3 Demon Dogs in large form
Defeat all Tin Soldiers
Complete Icy Flight without touching the ground
Collect 500 gems in Metalhead
Jump off every Supercharge ramp in Tree Tops
Detonate 3 explosive chests on the pillars in Alpine Ridge
Defeat all Metalback Spiders
Defeat hidden Egg Thief in Wizard Peak
Collect 400 gems in Blowhard
Defeat all three Ski Gnorcs
Unlock the strong chest in Doctor Shemp
Flame every Vulture in Cliff Town
Charge a Vulture
Take a trip with a Balloonist
Light the two bonfires in Dark Hollow
Glide to secret Egg Thief area in Town Square
Find the hidden entrance to Sunny Flight
Flame 10 sheep in Stone Hill
Do a loop around an arch
Use a cannon to dispatch a taunting Gnorc
Flame all Fairies in Night Flight
Charge through 4 Armored Druids near the start of Magic Crafters
Flame all Fairies in Crystal Flight
Flame 5 Glowing Mushrooms in Beast Makers
Light 3 fireworks within 15 seconds
Free a trapped Chicken
Complete Wild Flight without touching the ground
Complete Gnorc Cove without killing any Rats
Destroy 6 gears in Twilight Harbor
Get Gnasty Gnorc to complete 5 laps
Do not feed the Hungry Idol any red fish
Charge a Goat in Colossus
Headbutt every turtle in Turtle Soup challenges
Don't touch the lava in Skelos Badlands
Don't get hit by Bob
Defeat every Earthshaper in Fracture Hills
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 every Robo Bee by spitting
Mushroom Speedway: Fly Through 4 Star Speed Boosts In One Lap
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
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