The Riddler has hidden the required games for his trophy behind--what else?--riddles!  Once you think you have uncovered a game's title, there is a simple way to figure out if you are right:

First, find the game's individual game page by searching for it.



Click on the game to open its game page.



Click on the "Community Info" tab.  If a game is one of The Riddler's required titles, "The Riddler" will be listed here.



(Please note: Peggle is not a required game for The Riddler, it is merely being used as an example.)