Homer is a writer - so I am not sure which of his works you are referring to. But, if it's The Illiad, then one important character is Achilles.
1) His most important action is to kill Hector during the Trojan War - this leads for a definitive victory for the Greeks over the Trojans - it allows them to finish the long-term enterprise .
2) His dominant motivation is to seek revenge for the death of his close friend Patroclus. It is not honourable when considering that he should have been fighting primarily because he had previously agreed to help his allies. It is self-centered and unjust because Patroclus was killed during war and not on purpose. He also dishonours Hector's body after he has been killed.
3) Achilles is self-centered but loyal . He is also moody and belligerent but he believes he has been wronged. Overall, I have a negative impression of him based on this text.