Odysseus demonstrates heroic, god-like qualities throughout The Odyssey. In one instance, he cleverly tricks and blinds the Cyclops Polyphemus, saving his crew from certain death. Odysseus also bravely travels to Hades to learn his fate. Upon reaching Ithaca, Odysseus takes on all of Penelope’s suitors, defeating them to reclaim his rightful place.
Odysseus demonstrated god-like qualities in The Odyssey through his intelligence and ability to inspire his men.
In one instance, he tricked the Cyclops Polyphemus by telling him his name was “nobody” and then disguising his men as sheep so that Polyphemus would unwittingly let them out of his cave.
He is able to keep his men together for most of the story by earning their loyalty and devotion. Even in the face of dangers such as Scylla and Circe, the men stick with Odysseus.
Finally, at the end of the story, he tricks the suitors by doing what no other man can do: string his famous bow. In so doing, he has given himself the weapon with which to defeat the suitors and taken them by surprise.
Odysseus' encounter with and escape from the Cyclops, Polyphemus, in Book 9 is considered to be his most significant achievement because he not only saves himself but also a number of his men through his cunning and intelligence--with one exception. Initially, he tells Polyphemus that his name is Nobody or Noman because he needs to remain anonymous in order not to evoke any retribution from any of the gods, like Poseidon, who are already trying to destroy the man known as Odysseus. When he finally tricks Polyphemus into letting him and his men, disguised as sheep, escape from Polyphemus's cave, Odysseus cannot keep from telling Polyphemus who has actually defeated him:
'Cyclops, if any one asks you who it was that put your eye out and spoiled your beauty, say it was the valiant warrior Ulysses, son of Laertes, who lives in Ithaca.' (Book IX)
This disclosure has been roundly criticized by readers and critics as an example of Odysseus' pride, and it is surely an instance in which Odysseus' pride overcomes common sense. As several critics have pointed out, however, disclosing his real name is an act of heroism and defiance--Odysseus, as one of the leading warrior-kings in the Trojan War, could not let his triumph over Polyphemus be a mystery. Fame and honor are an essential part of a warrior-king's being, and Odysseus' defeat of such a formidable opponent as Polyphemus had to become part of Odysseus' recorded achievements even if the disclosure of his name put him and his men at risk.
A second episode depicking Odysseus' heroic nature occurs when, in Book 11, Circe tells Odysseus to journey to the underworld, Hades, in order to question the dead prophet, Teiresias, about Odysseus' fate. A journey to Hades, especially for a living person, is incredibly dangerous, and there are only a few heroes who have made the attempt--Hercules, Achilles, Aeneas--because they face the real possibility that they will be forced to remain in the underworld. Because there is no guaranty that Odysseus will be able to ascend to the living world, Odysseus is risking his life, just as he did many times over during the Trojan War.
In Book XVII,when Odysseus returns to Ithaca in the disguise of a beggar, he purposely faces the suitors as a beggar in order to understand what he will face when he finally takes his revenge on those who have defiled his household. At one point, he gets into a verbal altercation with Antinoos,one of the suitors, who throws a wooden stool at Odysseus, which hits him in the back, and Odysseus' response to this insult is:
Ulysses stood firm as a rock and the blow did not even stagger him, but he shook his head in silence as he brooded on his revenge. (Book XVII)
Anyone but a true heroic figure, who is biding his time in order to exact a final revenge on all the suitors, would have immediately engaged Antinoos. Odysseus, however, using the discipline honed through many years of warfare, ignores this insult because, as a warrior king about to retake his kingdom, his ultimate goal is much more important than responding to a single insult.
Odysseus demonstrates his heroic nature throughout the Odyssey in both significant and insignificant episodes, and personifies the virtues of a Bronze Age warrior king, with the addition of intelligence and endurance, attributes that allow him to survive long enough to retake his kingdom.
Here's short video that provides an overview of Odysseus's deeds: