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