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.
Light 3 fireworks within 15 seconds
Charge through every Monkey in Mystic Marsh
Defeat the Ox without taking a hit
Icy Peak: Destroy 6 icy things using the cannons
Lost Fleet: Use cannons to shoot down all vultures
Frozen Altars: Use ice breath to freeze 12 enemies
Defeat all Draclets in one Superflight
Don't hit any Sheep in Cloud Temples
Complete Gulp's Overlook without harming fodder
Don't get hit by Bob
Don't touch the lava in Skelos Badlands
Complete Crush's Dungeon without hitting any fodder
Heat up the audience
Headbutt every turtle in Turtle Soup challenges
Charge a Goat in Colossus
Do not feed the Hungry Idol any red fish
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
Flame 5 Glowing Mushrooms in Beast Makers
Do a loop around an arch
Flame all Fairies in Crystal Flight
Flame all Fairies in Night Flight
Charge a Vulture
Use a cannon to dispatch a taunting Gnorc
Unlock the permanent Super Flame
Defeat every Robo Bee by spitting
Defeat 5 Buggies while charging
Flame the Pigeons first in Metro Speedway
Defeat the Snowmobiles before defeating a Hang Glider
Don't touch the hazardous water in Shady Oasis
Defeat every Earthshaper in Fracture Hills
Use all 3 types of power-ups in Ripto's Arena
Headbash every rock in Winter Tundra
Steal a Popcorn Crystal from Hunter
Clean run in the trolley
Complete the long glide to Orb in Autumn Plains
Use a cannon to defeat a TNT thrower
Destroy every Roboshark
Defeat every robot in Hurricos
Complete Hunter's challenge
Light 6 Gem Lamps in 15 seconds
Midnight Mountain: Get revenge on Moneybags
Bugbot Factory: As Sparx, defeat the Metapede
Sorceress's Lair: Defeat The Sorceress
Dino Mines: As Agent 9, defeat an enemy with a ricochet shot
Haunted Tomb: Destroy All Sarcophagi
Crystal Islands: Defeat all the Crystal Bears
Desert Ruins: Find both butterfly jars
Harbor Speedway: Find Hunter
Starfish Reef: As Sparx, defeat the Manta Ray
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
Charmed Ridge: Defeat a giant
Fireworks Factory: Defeat Twin Dragons (Boss)
Spider Town: As Sparx, defeat the Spider King
Country Speedway: Fire 5 missiles in one race
Bentley's Outpost: As Bentley, destroy all the totem poles
Evening Lake: Free Bentley the Yeti
Honey Speedway: Fly through 12 star speed boosts in one race
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
Enchanted Towers: Destroy all the balloons
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
Seashell Shore: Defeat Bluto's nuclear shark submarine
Sunny Villa: Defeat all Coward Rhynocs
Sheila's Alp: As Sheila, destroy all headbash treasure chests
Sunrise Spring: Free Sheila the Kangaroo
Molten Crater: Unlock the locked treasure chest
Cloud Spires: Glide for 5+ seconds (and land safely!)
Collect all gems in Gnasty's Loot
Unlock Gnasty's Loot
Defeat 4 Nightmare Beasts in one glide
Charge through 3 Armored Fools in a row
Defeat 3 Demon Dogs in large form
Charge through 4 Puffer Birds in a row
Defeat all Tin Soldiers
Collect 400 gems in Blowhard
Free a trapped Chicken
Jump off every Supercharge ramp in Tree Tops
Complete Wild Flight without touching the ground
Collect 500 gems in Metalhead
Defeat hidden Egg Thief in Wizard Peak
Charge through 4 Armored Druids near the start of Magic Crafters
Defeat all Metalback Spiders
Detonate 3 explosive chests on the pillars in Alpine Ridge
Defeat all three Ski Gnorcs
Unlock the strong chest in Doctor Shemp
Flame every Vulture in Cliff Town
Take a trip with a Balloonist
Flame 10 sheep in Stone Hill
Light the two bonfires in Dark Hollow
Defeat Toasty without getting hit by him
Glide to secret Egg Thief area in Town Square
Find the hidden entrance to Sunny Flight