Ranking the heroes on this list is hard. Achilles was the greatest hero to the Greeks in the Trojan War, but Hercules overcame so many obstacles that it is hard to rank him second to any. Besides, in Iliad INestor says that all the heroes of the Trojan War are second rate compared with earlier ones like Theseus. This list is mine, however, and 21st century prejudices are in play, so Achilles supersedes Theseus. In this list I will show the major claim to fame of each of these heroes.
Hercules was outwitted by his nemesis Hera from before the time he was born. After his birth she tried to destroy him by putting snakes in his crib, but he was too powerful even then. He grew up to become the hero who beat the odds time and again, performed amazing, often helpful tasks, and yet was full of human foibles, even to the point of having to expiate the horrible crime of murdering his own children (under the guidance of Hera, of course).
Achilles was the Greek's best warrior in the Trojan War. His nymph mother, Thetis, held him by his heel when she dipped him in the River Styx. This left him vulnerable in one spot on his body. When he fought in the Trojan War he was unbeatable, until the gods guided the hand of Paris to shoot an arrow into Achilles' heel.
Theseus was the hero of the Athenians who saved them from having to send human sacrifice to the minotaur. He volunteered to feed the half man-half bull beast in the labyrinth. With the help of the creature's half sister, Theseus was able to slay the monster and find his way out again.
Odysseus was the wily hero of the Greeks who was considered by them second to Achilles. Odysseus was the one who came up with the idea of the Trojan Horse. He was also one of the few Greeks to reach his homeland of Ithaca, after 10 years of war and 10 years of troubles at sea. He was a descendant of Hermes, god of thieves.
Perseus was the son of Danae and Zeus. For a hero, having Zeus for a father was not unusual, but Zeus impregnated his mother as a shower of gold. After a bleak childhood, Perseus was helped by the gods to obtain the deadly head of snaky-tressed Medusa. With the help of her head he could then turn anyone he wished to stone.
Public Domain. Courtesy of Marie-Lan Nguyen/Wikimedia Commons.
Jason was another hero with an unfortunate childhood. To win back the throne he rightfully should have had, he was sent to capture the golden fleece. He set out with a band of the greatest heroes the world has ever known and had a series of adventures worthy of epic. Eventually, with the help of the witch Medea, he took the fleece.
Bellerophon is a little short of status among the heroes. He rode on the winged horse Pegasus; killed the Chimera monster, and tried to fly Pegasus to Olympus.
Orpheus is a hero for two reasons: he was counted among them in the Golden Fleece quest of the Argonauts and he survived a quest that even the more obviously heroic Theseus failed. Orpheus went to the Underworld to retrieve his wife, Eurydice, who had just died of snakebite. He made his way to the Underworld's royal couple, charming all in his passage with his extraordinary musical skill. Then Orpheus persuaded Hades to give him a chance to bring his wife back to life. He got permission -- on condition that he not look at Eurydice until they reached the light of day. While Orpheus failed to accomplish his mission, he returned to life without need of human intervention.
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