Now you can finally take care of Penguin #1 and luckily it won't be very hard. Run towards him #2 slaloming or evading often, so that he can't hit you.
Once you approach him, use the well-known skill Beat down, leading out fast attack by rhythmically pressing X #1. Before you is a whole series of cutscenes. Eventually it will turn out you have to find the body of Ra's al Ghul and use his blood to create the cure. In order to find al Ghul, you will have to follow the trace of one of his assassins #2.