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 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
Find all the cats
Find 100 cats
Find 50 sea shells
Find all the cats and all the sea shells
Turn the stone cats around
Solve the puzzle with paw prints on 3 rocks
Open the door by the beach
Open the yellow door
Find a gold starfish on a boat
Reach the party level
Reach the camp level
Reach the last level