The myth of Achilles in Greek mythology tells the story of a hero that was bathed in the River Stix by his mother, who held him by the heels. While the rest of his body became immortal, his heels did not. Later, he was wounded by an arrow in his heel, his only vulnerable spot, and died from that wound.
As an epithet is a descriptive word or phrase that sometimes appear in place of a person's name, an apithet about Achilles would be related to his story and attributes. So the correct passage is "He ceased; a gush of grief began to rise". It mentions his death--"he ceased"--and the gush of grief that also represents his bleeding wound.
