Here is the full list of all 23 Summer Paws achievements. It takes around 2-3 hours to unlock all of the achievements on Windows.
Find a gold starfish on a boat
Find all the cats
Find all the cats and all the sea shells
Reach the last level
Open the yellow door
Solve the puzzle with paw prints on 3 rocks
Reach the camp level
Find 100 cats
Reach the party level
Turn the stone cats around
Find 50 sea shells
Open the door by the beach
Find 50 cats
Reach the lighthouse level
Find a penguin at the fair
Find 25 sea shells
Open the green door
Find 25 cats
There's a rabbit near a greenhouse
Find 10 cats
Find 10 sea shells
Solve a stone statue puzzle
Find a sea shell