Speak with Shinjiro at every opportunity. The more you speak with him, the more you will raise your connection level with him. After October 4th, in-game time, you can begin dating him if you have spoken with him every time you could.
When can you hang out with Shinjiro?
Shinjiro represents the Moon Arcana Social Link for the female protagonist route, and expands his and Akihikos character past their subplot. It is available through the month of September starting September 7 on Mondays, Wednesdays, Fridays and Saturdays until the October Full Moon Event on October 4.
Can you date Akihiko In Persona 3 Portable?
User Info: thetruedemon. Get a device to go inside your PSP, then make Akihiko attracted to men. You have to pick four very specific conversation choices in his link. Its very easy to miss, sadly =/