Judgment

This achievement is very missable in the sense of these cats will only spawn in during the main story during investigations and if you even miss one you will have to go for this achievement in your next playthrough. If you happen to miss one during your playthrough you will have to find all the cats again. So, just trying to find the cats you missed in your past playthrough won’t unlock the achievement in your new playthrough.

There are 28 cats that can be found in Judgement during investigations but only 14 of them are actually in the main story (which are the ones we need) the other 14 are found during side cases. I’ll leave a video here for all the people who prefer video guides over written guides.
Here is a guide of when in the chapter you can find the cats with the objective name and a photo of where they are. (Note: Most of this information comes from powerpyx’s guide I used when I played the PS4 version of this game. Here’s a link to their guide. They had a pretty good achievement roadmap as well. https://www.powerpyx.com/judgment-stray-cat-locations/)
(Note: Sorry if some of the images are a little blurry a lot of the photos from powerpyx guide are small and probably don't translate well on TA)

Chapter 1:
2nd Active search: Locate your drone
You can find this cat almost immediately because it’ll be right in front of you on top of an Air Conditioner Unit


3rd Active search: Outside Amour “find the security camera”
Once you start the search immediately turn around and the cat will be in a doorway to the left


4th Active search: Outside KJ Arts “look for Kaito”
Turn back to where the door is to KJ Arts is and look on top of a vending machine to find the cat.


1st Drone search: After meeting with Kaito outside KJ Arts “use the drone to find Murase”
You’ll find the cat sitting at the top corner of the KJ Arts building sitting on the ledge.


5th Active search: Inside KJ Art in the security room “Turn on the room lights”
Look to the left window and outside the building door, you will see the cat.


6th Active Search: Outside Kyushu No. 1 Sushi “Find the security camera”
At the South end of the Alley, just outside the boundary for where you can walk


Chapter 2
1st Active search: Location of the second serial murder “investigate where the corpse was found”
On the left side from the entrance, on the ledge above the yellow crates

Chapter 3:
No Cats

Chapter 4:
1st Active search: In Genda Law Office, “Clear Hoshino-Kuns Name”
Look out the window and across the street, the cat is sitting on the power box in-front of the blue garage door


Chapter 5:
1st Active search: In Yagami Detective Agency verification mission “Investigate Shitani’s corpse”
To the left of the body look out the window where the record player is and across the street, the cat will be located in the entryway across the road.

2nd Active search: At the ADDC in the flashback, Verification mission “investigate the bed”
Head over to the window and look down and to the right, to where the pillar is under the sky bridge is at. Look at the base of the pillar to find the cat.


Chapter 6:
No Cats

Chapter 7:
1st Active search: Investigate Kaito’s Ruckus “search for clues about the attackers”
Head to the back of the area near the truck, and on the left behind the knocked-down sign you’ll see the cat.


Chapter 8:
1st Active search: Search mission “Search for three outlets”
On the opposite side of the room where you start at you can see the cat just underneath the gap in the blinds on the left window pane.


Chapter 9:
1st Active search: Search mission “Find Shono”
Look to your right and head towards the window, you should spot the cat sitting outside.


Chapters 10-12:
None of these chapters have cats in them

Finale Chapter:
1st Active search: Search mission “Find the gold keycard”
To the right of the bridge leading to the research wing, on the ground by the tree.


That should be your last cat for unlocking this achievement. If for some reason you did not unlock the achievement one of 2 things happened. You missed a cat during the story or the game glitched out. If your game glitched out try full restarting the Xbox or try loading a previous save and find the cat again.