Ra's al Ghul and the first appearance of his daughter, Talia, in "Into the Den of the Death-Dealers!"
Batman is on the trail of Dr Darrk - a member of the League of Assassins. A battle with some of Darrk's henchmen leads Batman to a small Asian Island, where he confront's Darrk, but is immediately surrounded by an insurmountable number of hoods, who overcome the Caped Crusader by sheer volume of numbers. Taken to Buddhist monastery, Batman wakes up to find himself unmasked and being tended by a young woman who reveals herself to be...Talia Al Ghul...daughter of Ra's Al Ghul. Turns out Darrk and Ra's have had a difference of opinion and Darrk has taken Talia hostage as well.
Darrk's idea of sport is to tie talia to a pole in the middle of a bull fighting arena and let the bull loose - giving Batman the option of running or trying to save Talia. He chooses the latter and succeeds! On the trail of Darrk once more, Batman and Talia finally confront him by the local railway line. In the ensuing battle, Talia shoots Darrk, who falls to his death in the path of an oncoming train.
In the second story, Batgirl finds herself captured by an underworld mob, and in a seemingly inescapable trap. Just as things seem to be getting desperate, one of the gang members returns to free her as he couldn't face a murder rap. Instantly, Batgirl gets on the trail of the gang who are about to commit a murder, which she prevents.