Here is the full list of all 24 Cats in Time achievements. It takes around 4-5 hours to unlock all of the achievements on Windows.
Fly away!
Find the secret level.
Collect every cat in the game.
Collect all postcards pieces in the game.
Korben, is that you?
Found him!
Forge the sword.
Everyone needs some help.
Visit every underwater location.
Visit (almost) every location in the game.
Visit every period in the game.
Visit every Tokyo location.
Visit every New York location.
Visit every wild west location.
Visit every German location.
Visit every Greek location.
Visit every ancient Egypt location.
Catch some fish.
Solve level without any hints.
Wow, that was quick!
Collect all cats on one level.
I knew it!
Destroy everything!
Do nothing and enjoy the moment.