Before you can do any of this, you will of course need to have unlocked the DEMO THEATER mode under EXTRAS in the main menu by completing the game once.

Enter the DEMO THEATER mode, and play multiple EVA focused cutscenes in succession.
I was able to unlock this by playing these three demos in a row:

• Contacting EVA
  
• Meeting up with EVA in the Mountains
  
  
• Meeting EVA behind the Waterfall 1
  

The Peep Demo Theater should then unlock and appear at the top right corner of the room.


Enjoy! 😉

(P.S. - Make sure to make an autosave afterwards in the main game by moving to a new room so it stays unlocked!)