Successfully complete Story mode under the Detective difficulty setting.
Madame Fate's Predictions
Completing the investigations on Ron N. Hyde, Justine Time, and Manni Cotti to get a note with a riddle. You will also have a choice between six rooms. Return to the study. The Crime Computer will alert you to something else in the room. Select the blue area at the filing cabinets to the right of the fireplace to find a crystal ball and Madame Fate the fortune teller. Tap on the Crystal Ball to get various messages from her.
Minigame mode
At the start of chapter 6 (the Heir hunt), you'll be tasked with completing a simple DNA minigame. Once you've completed it and made it back to Phil's dossier, close your DS. That's right, close the thing. (as if you're going to put it into standby mode) When you open it next, you'll be staring at the back cover of the dossier. Here, you can play either the DNA minigame or Tic-tac-toe, or go visit Madam Fate. (if you found her at the end of chapter 4) To go back, just tap the left-pointing arrow at the bottom left, which will bring you back to the dossier proper. You can go back to this area whenever you want (provided you're on either chapter 6 or 7) if you're not already investigating a suspect.
The Hitchhiker's Guide To The Galaxy reference
When you start the Astromalgy level, you should see the number 42 which, according to The Hitchhiker's Guide To The Galaxy, is the meaning of life, the universe, and everything.
Treasure Hunt mini-game
Successfully complete Story mode under the Detective difficulty setting.