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