Follow the only possible route heading north and afterwards turn east. Eventually you will reach a ladder #1 leading to the Chamber of the Demon. Watch a cutscene involving a slowly weakening Batman and afterwards head north #2.
You need to reach the big gate #1. A cutscene involving Talia al Ghul will be played. Batman will tell her that he wants to join the League of Assassins, which involves passing the Demon Trial. After the conversation ends, follow Talia using the newly unlocked stairs #2. After getting downstairs you will watch yet another cutscene.