The Hermit Arcana
The Hermit Arcana can only be accessed once Junpei gives you the MMORPG Innocent Sin Online on 4/28. After this you'll be able to initiate the Hermit Social Link by selecting "Play the MMORPG" instead of study when you're at your desk. It's worth noting too that you will only be able to play the MMORPG with Maya when you have off from school entirely and it will take up the whole day.
What I mean by off from school entirely is either a Sunday or a Holiday. You won't be able to raise this Social Link after school or during the Evening. You'll only have the option to play the MMORPG when it's "Daytime".
The ingame character behind 'Maya' that's associated with the Hermit Social Link happens to be Isako Toriumi, a teacher of Composition at Gekkoukan High. She doesn't introduce herself until the very end of the game and never mentioned her secret identity to you at school.
It's important to note that you can only access The Devil Social Link by first advancing The Hermit one to rank 4 or 5. You'll know you've unlocked the Devil SL once Maya tells you about the mean old man who harassed her at the Paulownia Mall one evening. For more information on this Social Link check out the Devil page.
While raising a Social Link you'll be given story cut scenes where you'll have to answer questions. The answers to each of these questions is different depending on the person and the situation. What you usually need to try and do is pick an answer that reflects their personality. Here's a cheat sheet for each Social Link rank of the Hermit Arcana and what to say.
Rank 1: Automatically earned
Rank 2: Of course - Outside is overrated
Rank 3: Oh really? - So you don't like your job?
Rank 4: Why don't we get married?
Rank 5: Don't you mean S.o.b? - Are you a teacher?
Rank 6: Which bastard?
Rank 7: Guys only go for younger chicks - Anything
Rank 8: Hurry up and tell me already - What's he like?
Rank 9: No way! - Anything works - What are you planning?
Rank 10: Automatically earned
When you finish this Social Link you'll be able to fuse Arahabaki through Cross Fusion using Kikuri-Hime, Okuninushi, Take-minakata and Omoikane.