You must now begin moving north-east, towards the passageway leading back to Arkham North. Batman will probably encounter two groups of inmates along the way. The first group will be small, however the other one is considered to be a serious threat.
Keep heading towards a large door and then go through a short corridor. Instead of using a second gate proceed to your left. Open a small door in order to be transported to Arkham North. Head south-east and get ready to defeat a new group of thugs along the way. It would also be a good idea to surprise them using the Glide Kick ability.
Once you've dealt with all enemy units head south and use your hook to climb over a large brick wall. You may now proceed towards a nearby entrance, leading to a small cave complex. You'll have to use your hook several times while inside the caves, as well as open a new door. A cut-scene will be displayed on your screen upon your arrival in a larger cavern.