Badges are little symbols of honor in Stray that let you walk around the city with pride knowing that you did a good job. These little tokens are the closest way you can customize the cat in Stray. There are a total of six Badges in the game that you get by completing various stages in the story as well as completing small side quest-type tasks for some of the robots you meet along the way. Getting them all will get you the Badges trophy as well.
Possibly the first of the Badges that you will get is the Outsider Badge. You obtain the Outsider Badge as part of the story. After you leave the Slums with Seamus to look for Doc, he will tell you that he can’t continue onward. When this happens, he will give you the Badge to show you are a true Outsider.
Also found in the Slums, you can get the Music Badge from Morusque if you help him out by finding all of the Music Sheets. There are a total of eight Music Sheets to find for him. Doing this will also get you the Meowlody trophy.
Outside of the Slums, after braving the sewers, you will come across Antvillage. This shanty town is home to many interesting robots like Malo. Malo loves to grow plants but they are missing three of them. If you manage to find the Red, Yellow, and Purple Flowers that they are looking for, they will reward you with the Plant Badge.
Once you reach Midtown, follow the main road until you reach a robot wearing a white ski jacket. He will be angry with a store clerk. Go inside the store and open the safe. The code can be found on the sign on the back of the shelves in the store. The code is written backward so make sure to type it in correctly. Inside the safe is the Cat Badge.
Go down the alleyway next to the clothing store in Midtown. Climb up the various objects along the walls to reach the barred window high up toward the rooftops. Jump through the window to find a dead robot with the Police Badge.
After breaking into Neco Corp, progress through the building until you find a worker robot who is searching with a light. He will tell you he lost his keys. Progress further through the area until you reach the room where you need to hide behind moving trash containers to avoid detection from the Sentinels. At the end of the first room, you will see some barrels that you need to use to cross some water. The worker’s keys can be found in a pizza box on the right side of the barrels. Bring them back to him to get the Neco Badge. If you got all the prior badges, you will also get the Badges trophy.