As Achilles chases Hector around town, Hector taunts Achilles and makes Achilles angry. After countless hours of chasing Hector, Achilles gave up chasing him and starts to taunt Hector.
Hector you coward, all you do is run like the bug that you are. Stand and fight like men if you are a man.
Hector turns around and says:
I am a coward and a bug I shall keep running until you give up on taking revenge.
As Hector says this to Achilles, Achilles gave out a loud shout and once again tries to catch Hector but it was no use, Hector was too fast, so Achilles withdraws to come up with a plan to catch the slippery bug.
Hector as you are too fast like a frightened prey I will let you live for a little longer until you have gained the courage to face me. I shall withdraw, but next time when we meet you won't be so lucky and fast as you are today.
Hector gave out a loud laugh and tells Achilles that he has too much confidence in his strength, and is blinded by vengeance but Achilles paid no attention to his words and took off.
The next day a messenger came to Hector and tells him that his brother was slain by Achilles in battle. After hearing this Hector leaves to face Achilles in battle to take revenge for his brother.
Hector arrives at Achilles' camp and accepts Achilles' challenge.
As Achilles accepts the dual he ask Hector a question:
Why did you suddenly accept the dual knowingly you would be slain in battle?
Hector responds:
You killed my brother, who had nothing to do with this, what you did was unforgiveable, so il too will take revenge for my brother.
Surprised, Achilles laughed, and Hector is confused and angry.
Why do you laugh?
I have never killed your brother, but if that story is what brought you here, I thank the gods for bringing you here to your death. Maybe you were born with ill luck and you fate has been sealed by the gods.
As the shocked Hector falls to the ground he cursed the gods who had tricked him.
It's useless to curse the gods, get up and let us fight like men.
As the two men fought, Hector managed to cut Achilles with his first strike.
I managed to cut you first, now let us fight to our hearts content and destroy each other's lives.
As Hector is speaking he sees that Achilles is being healed and his injury is gone. To Hectors surprise he shouts:
You said to fight as men but what you meant was to fight like men and god, with this I am surely to lose, perhaps this fight is in the favors of all the gods, I was tricked into this fight and now I'm fighting a god, but no matter it must be my time to go so I will fight you even if I lose.
So the battle went on until Achilles managed to get Hector's armor off and Achilles pierced his spear into Hector's chest killing him instantly.
With this I had taken revenge for my dear friend Patroclus. I hope he would be proud and accept Hector's soul as a gift.