Walking at night you will meet a character running on a map. You need to meet him several times. At one point, you will need to click on the character.
After a few meetings, the girl will speak with you. In the conversation you will have a choice: “Keep the company” or “Help with the player”.
The player can be found in the merchant's shop in ramen (aka Shady). We buy a player, go for a walk at night, meet Mikasa (the girl) and give her the player. After that, she thanks you with the 18+ scene.
A few days later we go for a walk at night and stumble upon Mikasa. We find out the whole truth about her and then there is a choice: “Reject Mikasa” or “Accept what happened”.
If you choose Reject, you won't see her again.
If you choose Accept, she will be near the Orochimaru base every night, so you can have fun with her.