Here is the full list of all 74 Crash Bandicoot N. Sane Trilogy achievements. It takes around 40-50 hours to unlock all of the achievements on Windows.
Earn 99 Lives
Earn 30 Relics (gold or better)
Discovered the Secret Exit in Dino Might!
Earn 10 Relics (gold or better)
Just "forget" it. Repeatedly.
Fly, then die.
Unlocked the Secret Exit in Unbearable
Die.
Earn 21 Gems
Have your bazooka ready.
Discover a Gem Path after earning a Color Gem
Earn 13 Gems
Shoot a background UFO in Future Tense.
Discovered the Secret Exit in Road Crash
Earn 5 Relics
Defeat N. Cortex
Defeat N. Gin
Defeat 5 enemies with Coco's Savage Hurricane Spin
Defeat N. Tropy
Discover a Death Route
Defeat Dingodile
Defeat Tiny Tiger
Discover a "?" Bonus Path
Die as Crash.
Defeat the Komodo Brothers
Defeat 5 enemies with Coco's Double Leg Drop
Don't feel guilty about jumping on him.
Defeat Ripper Roo
Seek and destroy
Earn the Key in Jaws of Darkness
Earn the Key in Sunset Vista
Defeat N. Brio
Spin away an Extra Life
Defeat Pinstripe Potoroo
Defeat Koala Kong
Miss a lot of boxes.
In a single level, spin an enemy into another enemy twice
Defeat 5 enemies with Coco's Spin
Defeat Papu-Papu
Enter a Bonus Round after collecting 3 Character Tokens
Earn 26 Gems
Earn 26 Relics (gold or better)
Discover the Secret Exit in Air Crash
Discover the Secret Exit in Bear Down
Discover the Secret Exit in Diggin' It
Unlocked the Secret Exit in Hangin' Out
Earn 42 Gems
Earn 27 Relics (gold or better)
Shoot the Imposter
Shoot 5 of them in a single level.
Earn the Gems in the bonus levels
Avoid whatever he's flinging at you.
Do hard time
Seek and destroy. Again.