This achievement is achieved for unlocking the secret minigame Think of the Children.
This minigame is unlocked by collecting the nine disc pieces that are scattered all over and around the ship:
1.In the main deck, climb up either of the two right-most masts to find the disc piece floating in the air.
2.Go to the Generator Room and jump over the gray and red blocks to the right to find a secret path to Benji's room. The disc piece will be lying to the right of the closet.
3.This disc piece is in plain sight in the Arcade Room, on a shelf on the right side of the room.
4.In the Lobby, go all the way to the right and make your way onto the left-most chandelier. From there, you can jump to a gap above the Costume Dept. door, which leads to a secret corridor with a disc piece inside.
5.Enter the Costume Dept. and jump into the gap on the right wall. Follow the corridor to find the Captain's Bedroom and the next disc piece.
6.In the level selection area, jump onto the middle-left platform and go left behind the curtain to find a secret area and a disc piece.
6.In the level selection area, jump onto the top-right platform and go right behind the curtain to find a secret area. Complete this platforming section to find the disc in the top-right of the secret room.
8.Enter the right door in the Legacy section. Leave this room to the right to find the next disc piece (116 stars required).
9.Jump from the deck of the ship and follow the path to the left. You'll find the last disc piece on the fourth screen (116 stars required).
Note that while you can already collect all but two of the disc pieces after earning 16 stars, you will need to finish the story (earn 116 stars) before you can collect the last two.
Once you have collected all disc pieces, enter Greatbeard Arcade from the deck and interact with the arcade machine for the achievement to unlock.