~K.K. Slider Rewards~
K.K. Slider’s badges are rewarded for the number of his songs you’ve listened to during his Saturday night visits. To get the gold badge you need to listen to 100 songs. There is no daily limit to how many songs count towards the badge, so you can stand in front of the stage and constantly ask him to perform songs making it possible to get the gold badge in as few as 1-2 Saturday nights, your own patience permitting.
K.K. Slider’s portrait is rewarded for attending 20 Saturday night performances. This means you have to visit him on 20 separate Saturday nights, so it should take a minimum of 20 weeks before you receive the picture.
However, there’s a workaround to this. If you have your inventory full when you first listen to K.K. perform on a Saturday, he won’t be able to give you an aircheck. If you continue to request songs from him while your inventory is full, the game counts each time as a new performance, as if you were listening on different weeks. Using this method it is possible to obtain K.K.’s pic within one Saturday night.
K.K.’s portrait will be delivered to you via a letter in your mail and is sent immediately upon hitting 20 performances. K.K. himself won’t let you know when you’ve got it, so you’ll just have to run back and check your house’s mailbox.