A hero is defined as a person, typically a man, who is admired or idealized for courage, outstanding achievements, or noble qualities. Gilgamesh and Odysseus are both considered heroes in my book because they both engaged on what would now be considered a 'typical' hero quest. They both took part in a journey away from their homes and their people to a strange place, or in this case, multiple places. While there, they battled great forces and defeated them. Upon their returns, they were both changed men, having learned something of themselves and the way of the world during their travels and challenges. They are ordinary men who have been granted certain strengths, one has physical strength and one has mental strength. They both experience hardships and make mistakes. They try to find themselves through life just like any average man.
Gilgamesh showed heroism when he defeated the monster called Humbaba. Humbaba was a giant creature that lived in the Cedar Forest. All who lived near this forest were intimidated, because this creature refused to allow anyone to pass through the forest. The people in Gilgamesh's hometown of Urok did not want him not to fight the terrible monster, and they were afraid that the battle would ultimately lead to Gilgamesh's death. Gilgamesh was very anxious for the battle with the monster, Humbaba, but he tricked him in a very clever way by offering his sisters to be the beast's wife or mistress. The creature was totally caught off guard by Gilgamesh's attack. Humbaba was beheaded. Gilgamesh was so crafty and determined which allowed him to kill Humbaba, which allowed for Gilgamesh to return home. Gilgamesh was a hero because he was not afraid to put his own life on the line for the sake of the others in his town. An example of how heroic Gilgamesh was is when he went on a voyage to the top of Mount Mashu. During this voyage, Gilgamesh showed his endurance and heroism because the cliffs were steep and impossible for mortals to climb.
