The cat is hidden outside of the store up on top of an adjacent business. To get it you will need to purchase a decoration of a train and place the ladder on top of it. Then you can climb up and jump over to the cat and pet it.
The achievement will unlock after you close your store for the night after you pet the cat.
Here are some links for a visual guide.
(Photos)
https://imgur.com/7tpM8a9https://imgur.com/wMXdzwKhttps://imgur.com/bwDIBwT(Video)
https://imgur.com/YXqkb5C