The Blood Trail
During the CS with Dr. Freeze we reveal that we have seen the formula before -- and that revelation is a calculated to cause the Assassin in the cage to react -- and she does! Now we have a blood trail that we can follow right to Ra's al Ghul!
Using Detective Mode you can follow the trail up the stairs and out the door. When you get outside hold down 'A' to request an equipment drop from Alfred so that the Line Launcher is on the way....
Following the blood trail is very easy in Detective Mode -- so really all that you need to do is follow the trail, stopping whenever you encounter a group of thugs with a Greenie in them, since you want to be collecting all of the data you can from them as well!
A Special Delivery
Eventually you will reach a rooftop where the blood trail is getting thin -- and that triggers a scanning event where you need to examine a bloody bandage dropped by the assassin which turns into a very brief CS that culminates in you being attacked by the assassin! You tell yourself that you need to plant a tracker on them if you are going to succeed in following them, which then prompts a chase from rooftop to rooftop (holding down 'A' the entire time to run and auto-climb) until you catch up and get close enough to plant the tracker.
The assassin is joined by confederates and has you by the throat with her sword when who should show up but the Boy Wonder himself! Robin! No worries though - he is just here to deliver the Line Launcher Gadget that Alfred promised you. This is an especially useful Gadget as it allows you to zipline horizontally -- if you played the previous game you know why this is a valuable tool, but if not you will soon learn why it is important...
You give him your blood sample to have analyzed and order the Boy Wonder back to Gotham proper, though clearly he would rather hang with you!
Eventually the trail will take you below ground -- but to get there you will need to take out some groups of armed thugs in the process so you will need to be careful. And good! Once you actually go underground and begin tracking the target through this area you will finally encounter the chattering teeth that were so familiar in the previous game -- just use your Batarang on any teeth you encounter along the way and eventually you will get them all!