The 2nd Island[edit]
After a scene in which Monomi alludes to a newly-unlocked mini-game, you'll be able to access a new area. Reach it by first going to Central Island, and then going through the now-open gate marked with a 2. Start by walking until you reach the Library.
Inside the Library are Peko and Sonia. Pan the camera up to the second level along the right wall to find Hidden Monokuma #1, then speak to the girls. The discussion with Sonia will shed some light on the history behind Jabberwock Island, whether it's true or not. Examine the statues and bookshelves, and eventually Sonia will start talking about serial killers. After that strange discussion, exit the Library and walk right to the Pharmacy.
Mikan can be found inside the Pharmacy, as well as Hidden Monokuma #2 behind a shelf to the right. Speak to Mikan for her take on the new location before continuing to the Diner. Return to the parking lot after speaking to Fuyuhiko, and examine the tunnel in the distance to find Chandler Beach. Walk past the Beach House and speak to Ibuki. After the scene, walk along the shore until you see Hidden Monokuma #3 floating along the end. Enter the Beach House and speak to Kazuichi. After Hajime is done speaking with him, Chiaki will enter to summon you to the Ancient Ruin. Once you have control again, speak to everyone before speaking to Chiaki to advance the plot. Then, examine the ancient ruin to get a closer look at it. Here, you can examine the door for a long scene, after which Hajime will end up back in his cottage with a lot of information to think over.
The game[edit]
Speak with the students in your path on the way to the Hotel Restaurant. After the group discussion, you'll have two Free Time opportunities to spend with any student except for Nagito and Fuyuhiko. An announcement from Monokuma will follow summoning everyone to Jabberwock Park. Go there and speak to everyone after the discussion concludes, then examine the arcade cabinet to advance the plot. The next morning, exit the cottage to bump into Fuyuhiko. He's holding a suspicious envelope, and is of course unwilling to divulge its contents to Hajime. Go to the Hotel Restaurant to find Mahiru, who pushes Hajime into bringing Nagito his breakfast. Head to the Old Building and then enter the Dining Hall after a short interruption from Monomi. After the scene, you'll have two more Free Time opportunities.
When night falls, head to Jabberwock Park and examine the arcade machine. In the game, walk right until you reach classroom 1-B. Examine the locker at the end of the room and then backtrack to classroom 1-A on the other end of the hall. When back in control, examine the locker at the end of this room to earn Monocoins. Then, speak to Girl B, located at the front of the group. The story quickly takes a dark turn, but it's not over yet. Speak to Girl D (second from the back of the room). After the scene, enter classroom 1-B. On that ominous note, the game concludes.
The next day, enter the Hotel Restaurant as usual. A Free Time opportunity follows, after which Hajime will end up at Rocketpunch Market automatically to speak with Kazuichi. After the conversation, go to the Diner on the second island. Speak to Kazuichi outside, then enter and speak to him twice to trigger a scene. Re-enter the Diner for another scene. Afterward, go to Chandler Beach and walk around to the other side of the Beach House, as the back door is mysteriously locked. Enter for a disturbing discovery.