This Achievement unlocks for feeding and petting the cat inside the Bakery.
You'll need to steal the key from the Baker's back pocket and use it to unlock the refrigerator in the storage room. Inside the fridge you can pick up the fish then place it in the cat's bowl.
After placing the food in the bowl simply press
on the cat to pet it and the Achievement will unlock.
For those who prefer videos here's my quick guide.