On 3/20 (March 20), go through town and talk to all the social links you have maxed out. After that is done the game will ask you if you want to go home, Select no then go to the Junes Food court. After the scene there go to the Samegawa Riverbank and talk to Dojima and Nanako. After that conversation go the velvet room. After that conversation go to the gas station nearby and talk to the attendant, make sure NOT to use answers that would end the conversation and only answers that pertains to the case and what you have learned. The Final Dungeon should unlock and upon its completion, the game will be over and this trophy yours.