Here is the full list of all 16 Purrfect Rescue achievements.
Rescue all the amusement park cats
Rescue all the cats
Rescue Snape
Find the Sardine
Rescue all the residential neighborhood cats
Rescue Marie
Rescue all the park cats
Find the Catnip
Rescue all the city center cats
Rescue Tilapia
Find the Cat Trap
Rescue Alemão
Rescue all the beach cats
Rescue Mama
Find the Feline Pheromone Bottle
Find the Anti-scratch Glove