Here is the full list of all 52 Crash Bandicoot 4: It's About Time trophies - there are 40 bronze, 9 silver, 2 gold and 1 platinum.
Get EVERY trophy
Watch the 106% bonus ending
Watch the 100% bonus ending
Earn ALL of the platinum Flashback Relics
Complete ALL levels in N. Verted mode
Earn ALL N. Verted Gems
Earn ALL of the Clear Gems
Earn ALL N.Sanely Perfect Relics
Do some target practice
Find the source of the Bumpa Berries
Make some noise!
Earn ALL of the platinum Time Trial Relics
Complete all Timelines
Earn half of the Clear Gems
Aim and fire!
Grabbed a bushel of Bumpa
Complete any Timeline
Beat any boss in N. Verted mode
Beat a level in N. Verted mode
Play a game of Crate Combo
Play a game of Checkpoint Race
Complete a level with Pass N. Play enabled
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
Meet Ika-Ika
Defeat Dr. Neo Cortex
Find the hidden Yellow Gem
Meet Kupuna-Wa
Scare the cat hiding from a party
Defeat N. Brio
Find the hidden Blue Gem
Shut N. Brio up
Meet 'Akano
Defeat N. Gin and his Weapon of Mass Percussion
Find the hidden Green Gem
Make music in an unlikely place
Earn any Flashback Relic
Acquire a Flashback Tape
Shut N. Gin up
Earn any Time Trial Relic
Complete a level as Coco
Try on a Skin
Find the hidden Red Gem
Meet Lani-Loli
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