Well, you can't exactly call Joan of Arc a mythological character, as she's widely considered to be a real live historical person. However, the stories around her have grown so much over the years that she's definitely taken on a legendary status and even been declared a saint by the Catholic Church.
Joan reminds us of Antigone in a lot of ways. The big one being that she was a woman who was way ahead of her time. Joan made a name for herself during the Hundred Years War, when she single-handedly rallied the dispirited French army into some major victories against the invading English and managed to finally put the throne of France back in French control. Like Antigone, Joan faced a lot of opposition from the men around her, even the ones she was trying to help. It totally blew these dudes' minds that a young girl would be able to succeed where so many men had failed before her.
Antigone and Joan are also similar in that they followed a higher moral code of their own. Joan believed that she heard voices that came directly from God. It was these voices that inspired her to do all the heroic things she did despite all the opposition from the men around her. Antigone too shows a loyalty to the divine, when she argues that not burying Polyneices is an insult to the gods and uses it as one of her justifications for violating Creon's decree.
Unfortunately, these two tough ladies are also similar in that they died for their beliefs. Joan was eventually captured and sold to her English enemies. She was tried for heresy; her accusers said that she was a witch and that the voices she heard were from Satan instead of God. Though Joan did waver momentarily, in the end she stuck to her guns and refused to recant her story. In the end, Joan was burned at the stake as punishment, going to her death like Antigone for the higher cause she believed in so fiercely.
Click here to read all about Shaw's great play Saint Joan.