The main goal of Little Kitty, Big City is simple: reach the house you fell from. There are a few steps you need to go through, though, and an extensive walkthrough will help.
Little Kitty, Big City How to Get Home (Home Sweet Home Achievement Guide)
In a perfect world, a cat climbing a few ledges to get back to an apartment window should be a piece of cake—or in this case, a fish fillet. I don’t want to be catty about it, but it’s a little cattier than that, and we recommend holding on to your paw for some assistance.
A walkthrough of Little Kitty, Big City is just what you need, and you'll be snuggling up in your favorite sleeping spot in no time.
To complete Big Kitty, Little City, you'll need to find Shinies for Crow to get the first Fish. Collect the last three Fish to max out your Climbing Stamina and climb the building you fell from to complete the main game.