Polyxena was one of the two daughters of the king of Troy during the Trojan War (the other was Cassandra, who was taken as a slave by Agamemnon and who died with him in Greece at the hands of Clytemnestra's assassins, see the "Iphigenia" story for the background). After the war, it was presumed that Achilles' ghost was preventing the Greek ships from sailing home, and therefore the princess was offered to him as a sacrifice. The following account is based on Euripides, Ovid, and one of Picasso's drawings.
The whole army of the Greeks, drawn up in ranks, was present at the execution, waiting and watching as Polyxena was led slowly by Achilles' son through the center of the camp and up to his father's tomb. Allowing him to hold her by the hand, as if he were her father and was conveying her to her wedding, she accepted his assistance as she stepped up onto the burial mound. Talthybius stood nearby, while behind the girl came a troop of soldiers purposely appointed to prevent her struggles.
Then Achilles' son lifted a golden beaker to pour the offering of wine to his father's ghost and nodded to Talthybius to call for silence.
"Quiet, Acheans!" he shouted, "Silence in the ranks!" Instantly a hush fell on upon the army and Achilles' son began to pray.
"Great ghost of my father Achilles, receive this offering I pour to charm your spirit up. Rise and drink this gift we give to you, this maiden's fresh blood. Be gracious to us, set free our ships and loose our anchor-ropes. Grant to all of us our day of coming home, grant us all to come home safe from Troy!" So he prayed, and his army with him.
Then, grasping his sword by its golden hilt he slipped it from its sheath, and made a sign for the soldiers to seize her.
But, as they laid hands on her, she spoke. "Wait, you Greeks, you who sacked my city! Of my own free will I will die. Let no man touch me. I offer my throat willingly to the sword, I will not flinch. But let me be free for now. Let me die free, I am of royal blood, and I scorn to die the death of a slave!" Achilles' son didn't answer immediately, and she continued: "To whatever spirit you offer my blood, will it not be all the sweeter if it is freely given? Such is my offer!"
"Free her!" the army roared, and Agamemnon ordered his men to let her go. The instant they released their hold, she grasped her robes at the shoulder and ripped them open down the sides, exposing her naked breasts, bare and lovely like a sculptured goddess.
Casting her robes aside, she sank kneeling on the ground, and uttered her most heroic words. "Strike, captain!" she cried. "Here is my breast! Will you strike me there? Or in the neck? Here is my throat, bared for your blow!"
Torn between pity and duty, Achilles' son stood hesitating. After a moment, he drew back his sword as if to strike, but then he again paused, the sword poised. Polyxena watched his eyes and did not move.
"I must," he told her, his voice low, his tone apologetic.
Her eyes remained steady. "I know, captain." She rolled her shoulders back, throwing her breasts into sharp relief. "Pierce me, as we both know you must." She paused for a moment. "As we both know you will...!"
He nodded, and, with a final sigh, he drove his sword into her proffered breast.
True to her word, she did not flinch; she even leaned into his blow slightly. They all saw it strike, they all saw it bite cruelly into the smoothness of her left breast, a bit above the rosy nipple; they all saw and heard it tear its way deeply into her young and tender body.
Her head went back, her mouth flew open and her shoulders arched; Achilles' son stood frozen for a few seconds, leaving her impaled on his blade. Regaining her control, she looked down at the sword piercing her, then turned her eyes back to his face. A single line of bright red, originating where the bronze blade passed into her body, painted her nipple red. From there it trickled down over her breast, down her side, and onto her hip.
Then he pulled the blade free. Blood spurted out, splashing on the ground and flowing down over her still-lovely breast, coating it in hot wet redness. Polyxena started to fall. Talthybius jumped forward and caught her under her arms. She fell back against him, a steady stream of blood still pumping from her pierced breast. Talthybius held the dying girl gently, watching her face as she gasped for breath, as her life's blood poured out onto Achilles' grave. Her gaze moved from Achilles' son to Talthybius; there was no accusation in her eyes. Only at the end, when her death was almost upon her; only then did she finally turn her courageous eyes away.