I found the tales of Cu Chullain to be fascinating and enjoyable to read, despite the way that his violence is glorified and revered. He is portrayed as the ultimate Irish hero, with Herculean strength and the reckless courage of Achilles, indeed like Hercules and Achilles his name and reputation inspires fear in his enemies. Its hard to believe so many of his courageous feats were accomplished while he was only a child, including impregnating the fierce Scottish warrior Aife.
In my opinion many of Cu Chullains endeavours can be defined as heroic, he rescues his friend, King Conchobor from the battle against Eogan Mac Durthact (Kinsella, 80), singlehandedly defends the woman, and men in pangs against the twenty seven marauders from Faichi with only sticks and stones (Kinsella, 81) and after killing the hound in self-defence at the feast of Conchobor, offers to stand in its place and protect Culann, which is how he came to be known as Cu Chullain, the hound of Culann(Kinsella, 83).
From an early age he displayed his strength and fearlessness, challenging three times fifty boys on the fields of Emain and defeating them with nothing but a shield made of sticks. This was presumably where he first experienced Riastrad or Warp-Spasm, a hulk like rage (Kinsella,77).
With so many incredible feats already accomplished he continues to seek fame and glory, perhaps out of Narcissism and no doubt fuelled by his Godlike strength. One day while the Druid Cathbad was teaching his students druid lore, he overhears Cathbad say, If a warrior took up arms for the first time that day, their name would endure in Ireland as a word signifying great acts, and stories about him would last forever (Kinsella,83-84). Upon hearing this he tricks Conchobor into giving him his weapons and thus fulfilling the druids prophecy, though Cathbad warns him that while he may achieve greatness, his life would be short, to which he replies If I achieve fame I am content, though I only had one day on Earth. (Kinsella, 85) While all of this behaviour could be described as narcissistic, I think it is rooted in his sense of servitude and desire to protect and honor his King and countrymen, perhaps he felt he alone could defeat all of their enemies.
He showed other acts of heroism too in my opinion, despite his great strength, speed and skill he also showed mercy at times. Once in surrendering to his exiled former foster father Fergus if he would agree to do the same at time of Cu Chullains choosing. He repeated this again with his foster brother Ferbaeth, whom was sent by Medb to meet Cu Chullain in battle. Cu Chullain begged him not to fight him, ultimately Ferbaeth chose to honor Medbs request and forsake foster-brotherhood with Cu Chullain, leading to his death.(Kinsella, 128-130).
Ultimately, like so many mythological heroes before and after him , I think his pride and arrogance lead to his downfall. He had made so many enemies in his short life, who all conspired against him to relieve him of his spears, knowing this was the best and perhaps only way to kill him. Three times in a display of arrogance he gave up a spear by slaying one of Medbs satirists (Kinsella, 126). Elsewhere, Cu Chullain lost some of strength after being forced to break his geas after being forced to choose between being inhospitable to a woman or eating dogs meat. In his last battle he spies Morrigan, whom had earlier prophesied about his early death, charging into battle he was poetically slain by his own spear.
Kinsella, Thomas. The Táin: From the Irish Epic Táin Bó Cuailnge. Oxford University Press, 2002.