After getting the man to open the shutter, revealing more of the underground, go due west and into the garages to find an old woman. You can accept a quest from her. This quest will require you to have the camera from "Deliver the Film"'s completion.
Basically go take a picture of the bar in the Golden Gai area - go to the first area where you fought the Corpses, then north an area and east another. The bar itself is in the east side of the northeastern of the central buildings. Then bring back the pictures. The quest will reward you a massively useful five Ag Incenses !
"Ikebukuro Free District"
Once you enter "Shinjuku Station: West Entrance", you can go west and enter a room to find a man with another quest requiring the camera. It can't be done until you reach Ikebukuro - obviously - so we'll cover it in more detail when it's actually doable.
"Demon Guarding the Shrine"
This is the highest-rated mission so far regarding difficulty at 5.5/8 (or 6.875/10). Head along to Kasumigaseki via the Terminals and leave the Counter-Demon Force Base to the overworld map.
From there, head to the guide far to the north. Go along the next northbound road to the east and stop at the second place. (Be sure to save before entering.) Within is Okuninushi. Challenge him to battle, if you dare.
Offensively, this boss does not come off as strong as the Prima Guide says he does. His attacks usually center around 80 damage. One of the more notable ones is Dream Fist, which simply is Attack with a Sleeping side effect.
He also has Beserker God, which appears to be a multi-hit attack, although it always missed against me, so I couldn't judge its power. Mostly, just freeze him to death with Ice-based attacks - there is not nearly enough here to worry about that warrants anything other than an all-out tactic.
After the battle, you can get the Bushi Tasogear lower-body armor. It raises your max HP by 95 and Agility by 6 - a large improvement overall compared to whatever you probably have!