Here is the full list of all 23 The Purring Quest achievements. It takes around 3-4 hours to unlock all of the achievements on Windows.
Collect 200 fishbones in Level 3
Collect 1000 fishbones
Free all the caged cats
Free Sheldon
Play the piano game with less than 3 mistakes
Collect 200 fishbones in Level 4
Collect 200 fishbones in Level 2
Find Oskar's ties
Free Tonks
Break 10 vases
Throw 5 rats into the graveyard holes
Collect 200 fishbones in Level 5
Free Snicker
Find Nala's cup
Find Nora's score
Free Abb
Hit dogs 10 times
Jump over chihuahuas 10 times
Find Cooper's book
Throw 20 apples
Free Daisy
Collect 200 fishbones in Level 1
Find Henri's book