You go back to the dorm because of it being a full moon and the game automatically moves to the Dark Hour. Mitsuru and Akihiko talk a little bit before she finds a Shadow, a big one. You, Yukari and Junpei go on ahead and wait for Mitsuru to arrive in front of the station. Once she arrives, she'll mention that the Shadow is located in a monorail not too far from the station. Once you gain control of your character, simply move to the right until you catch up to the monorail.
Once you're near the monorail, you'll board it after some small chat. You'll be trapped inside the monorail and once you gain control, simply move forward until you encounter a cutscene. Junpei will run after the one Shadow and you'll be jumped by two from behind. Simply use Agi on the books to finish them off, then you'll get into a fight with two more Spurious Books and a Heat Balance (weak to Garu and Zio).
Once that battle is over, keep moving forward until you catch up to Junpei. You'll be thrown into a battle with three more enemies, so take care of them (Dancing Hand is weak to fire). After the battle, the train will start moving on its own and you'll get into yet another battle, but this time you'll see that a countdown has started (8 minutes). You have 8 minutes to get to the front car and quickly defeat the main Shadow, so quickly dispatch the three enemies and move forward. The rest of the enemies are now random and can be avoided, although it might be tough considering the size of the monorail. Once you get to the front, you'll get into a battle with...
BOSS - Priestess
- Skills - Physical (Pierce), Bufu, Mabufu, Assault Dive, Pulinpa, Marin Karin, Summon (Muttering Tiara)
- Spoils - Diamond
This is your very first storyline boss fight and it's not a real difficult one. Make sure you don't have a Persona equipped that's weak to ice, as the boss uses both Bufu and Mabufu. You'll also want a Persona that has access to Bufu, as the boss can summon Muttering Tiaras to help, which are weak against ice. The boss does not have a lot of HP, but has enough where the battle is prolonged. If it uses Marin Karin or Pulinpa, make sure you cure it as soon as possible. This battle is only difficult, really, because of the time limit. It might help if you have both Orpheus and Apsara, since you can use Cadenza to heal.
After the battle is over, your Fool Social Link will increase to level 3 and you will learn a new Tactic for your teammates, Conserve SP. You will view some more cutscenes, then the next day will arrive. Note that you will always be tired the day after a full moon, no matter what.