The Sacrifice of Polyxena, about 1733-1734. Additional Info: According to Greek legend, Achilles fell in love with the Trojan princess Polyxena, the daughter of the king of Troy. He was offered her hand in marriage if he agreed to end the war between the Greeks and the Trojans. At Polyxenas request, Achilles came to make a sacrifice to Apollo, but he was ambushed by Paris, Polyxenas brother, as he knelt at the altar. Paris shot a fatal arrow into Achilles heel, his one vulnerable spot. Before he died, Achilles vengefully proclaimed that the treacherous Polyxena be sacrificed at his tomb.