Complete the indicated task during the main storyline to unlock the corresponding mini-game.

Mini game	How to unlock
Beach Volley	Win the match in Chapter 4.
Poker Game	In Chapter 5, select the second option from Itsuki to get rid of him, then select Mikuru and finish with an "SOS Grade" rank.
The Day Of Sagittarius 3	In Chapter 5, select the second option from Itsuki to get rid of him, then select Nagato and finish with an "SOS Grade" rank.