Yakuza 6: The Song of Life

To complete this achievement, you first need to approach and enter the Nyan Nyan Cafe, located inside the building complex on Senryo Ave, located to the left of the building that houses the Modern Mahjong establishment. The cafe is located on the floor above the Mantai Net Cafe branch for Senryo. When you head up the stairs to the entrance, you'll trigger a cutscene where a dissatisfied customer is leaving. Enter the front doors and go inside and approach the proprietor and he'll explain to you about the Cat Cafe sidequest, where you have to feed a stray cat you find a particular flavor of cat food they like to the point of filling up the Cat Friendship meter on the top left corner of the screen. Once it's completely filled, you'll get a cutscene of Kiryu calling the proprietor to come over and pick up the cat to bring to the cafe. Once the introduction to the sidequest is complete, it'll also complete the Look What The Dragon Dragged In substory.

Keep in mind, you can trigger this sidequest in Chapter 1, but cats won't be available for you to interact with until the following chapter. So progress through to the end of Chapter 1 first, and the first part of Chapter 2 where you investigate the hit and run and make chase against a Someya Family associate, before you are free to explore Kamurocho again.

There are nine cats in Kamurocho (as well as ten in Onomichi) for you to look. They pop up randomly in different spots, rather than always visible in the same location. The important thing to listen as you look is for a meow sound, meaning a cat is nearby, and you'll also get a bright blue circle to pop up on the map, meaning the cat is visible for interaction. Make sure you are stocked to the max on cat food, with a total of six flavors as well as a Gold Tuna flavor that all the cats like, albeit more expensive at 10,000 yen. You can carry each flavor up to ten cans each, and they can all be bought from the proprietor at the cat cafe.

Attached here is CryicZ's chart for the locations of all 19 cats, as well as their favorite cat food flavors. Bonito holds the greatest consensus for regular flavors among the Kamurocho cats with six of the nine reacting favorably. https://gamefaqs.gamespot.com/ps4/181153-yakuza-6-the-song-o...

You'll get the achievement to pop once you fill the Cat Friendship bar on the third cat you successfully recruit to the cat cafe. Happy exploring!

First, you have to go to the cat cafe and start the cat cafe substory.
There is a cat cafe in a building on Senryo Ave in Kamurocho
It is the place where there are many controller icons at the bottom right of the Kamurocho map.

Cats can be found at certain points on the map. If you hear a cat meow, look around.
Talk to your cat and feed it using canned food.
You can rescue cats by maxing out your friendship
Cats spawn randomly, so you can't always meet them.