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