Here is the full list of all 51 Crash Bandicoot 4: It's About Time achievements worth 1,000 gamerscore.
Watch the 106% bonus ending
Earn ALL N.Sanely Perfect Relics
Earn ALL of the platinum Time Trial Relics
Watch the 100% bonus ending
Complete ALL levels in N. Verted mode
Earn ALL N. Verted Gems
Beat any boss in N. Verted mode
Earn ALL of the platinum Flashback Relics
Make some noise!
Earn ALL of the Clear Gems
Complete all Timelines
Earn any Time Trial Relic
Defeat an enemy with Triple Spin
Pull off a Triple Spin
Defeat Dr. Neo Cortex... again.
Betrayed! By your worst enemy.
Defeat the Doctors N. Tropy
Grabbed a bushel of Bumpa
Play a game of Crate Combo
Play a game of Checkpoint Race
Beat a level in N. Verted mode
Meet Ika-Ika
Defeat Dr. Neo Cortex
Earn half of the Clear Gems
Meet Kupuna-Wa
Find the hidden Yellow Gem
Aim and fire!
Do some target practice
Scare the cat hiding from a party
Defeat N. Brio
Find the source of the Bumpa Berries
Find the hidden Blue Gem
Shut N. Brio up
Meet 'Akano
Complete any Timeline
Defeat N. Gin and his Weapon of Mass Percussion
Earn any Flashback Relic
Complete a level with Pass N. Play enabled
Find the hidden Green Gem
Make music in an unlikely place
Acquire a Flashback Tape
Complete a level as Coco
Shut N. Gin up
Try on a Skin
Meet Lani-Loli
Find the hidden Red Gem
Earn any N.Sanely Perfect Relic
Beat a story level without dying
Complete a Bonus Path
Crouch or slide into a double jump
Spend some time surfin' the waves