Achilles is discontent in the underworld, longing for life on earth. He says that Odysseus shouldn't try to "reconcile" him to death: Achilles would gladly go back to earth in the humblest of states rather that stay in Hades:

I’d rather serve as another man’s labourer, as a poor peasant without land, and be alive on Earth, than be lord of all the lifeless dead.

This is ironic, as Achilles was given the choice of being a famous warrior with a short life or an obscure person with a long and fruitful life. He chose fame and an early death, and now says he regrets the decision.

He also asks for news of his son, Neoptolemus. Odysseus is able to fill him in on some details, telling him that Neoptolemus is an eloquent speaker and the best of warriors. Odysseus speaks of his fighting skills and leadership, and says:

he begged me endlessly to let him leap from the Horse, toying with his sword hilt and his heavy bronze spear, eager to wreak havoc on the Trojans.

This feat did not lead to his death: instead, Neoptolemus killed many Trojans and took away his share of war spoils without ever becoming injured. This news makes Achilles very happy, and Odysseus can report that Achilles finally goes away pleased, walking with "great strides" and "rejoicing" in his son's greatness.

Achilles says he would be content to be on earth as a humble laborer, but his speech indicates his heart is still in warfare. He says he wishes he could return to earth for just one hour, so he could use his warrior strength to punish anyone abusing Peleus. He is also very proud of his warrior son.

In book eleven, Odysseus travels to the underworld to consult Teiresias's shade, which warns him to stay away from Helius's cattle on the island of Thrinacea and elaborates on his future exploits. Following his interaction with Teiresias's shade, Odysseus speaks to a series of female shades and Agamemnon's ghost before addressing the shade of the famous warrior Achilles. The legendary Achilles is one of the great heroes of Greek mythology, and he was renowned for his heroic performance in the Trojan War. In The Iliad, Achilles is portrayed as a courageous, petulant warrior who is extremely loyal and ambitious. In the underworld, the shade of Achilles remains a sulky, brooding character, but he now possesses a different perspective on legacy, fame, and glory.

Initially, Achilles's shade questions Odysseus's motivation for traveling to the underworld. Odysseus proceeds to explain his mission to address Teiresias's shade and proceeds to praise Achilles by rejoicing his impressive legacy on earth. Achilles's shade reveals his despondent, surly disposition by stating that he would rather be a slave on earth than the lord of the wasted dead. Achilles does seem to care about his legacy on earth and rejects his former desire to attain fame and glory. He is no longer the prideful, confident warrior he once was and possesses a dim outlook on his eternal condition. Achilles then asks Odysseus about his son and father and seems pleased by Neoptolemus's performance in battle.

Achilles's shade in the underworld is virtually identical to Achilles the mortal warrior. He's a proud, surly character completely at odds with his surroundings. Even though he's by far the most important shade in the underworld, he still hates the place with a passion. Odysseus is surprised that such a great hero, someone who achieved such remarkable feats of bravery on the field of battle, could possibly be so utterly miserable. But Achilles has seen heroism and its consequences from both sides, and so has a much deeper understanding of what it entails than the mortal Odysseus. Almost uniquely among the veritable cast of thousands in The Odyssey, Achilles challenges the dominant notion of heroism and its allied notion of glory. There's nothing glorious about Hades for Achilles, for as he tells Odysseus:

By god, I'd rather slave on earth for another man—
some dirt-poor tenant farmer who scrapes to keep alive—
than rule down here over all the breathless dead.

Achilles is dead by the time the action of the Odyssey takes place. Odysseus therefore meets Achilles when he visits the underworld. Just as he was when he was alive, Achilles is moody and brooding. He tells Odysseus that it is terrible to be a shade in the land of the dead. Even a revered ghost like him finds no solace in his fame. Achilles tells Odysseus that it is better to be a nobody, even a landless peasant, in the land of the living than a famous hero among the dead.

When we knew him in the Iliad, Achilles was a gloomy and ill-tempered teenager. Little has changed now that he is dead, other than that he does not boast like before. Gone are his pride and arrogance. Perhaps death has given him perspective that fame and glory are not the achievements that should be coveted most. Even though Odysseus does his best to cheer up Achilles, the dead warrior acts as despondent as in the Iliad when Agamemnon takes away Briseis, his war prize. Only now, instead of being angry, Achilles has resigned himself to being in this sorry state for all eternity.

Odysseus' meeting with Achilles in the Underworld is perhaps my favorite part of The Odyssey, as it's one of the most thought-provoking moments in the poem. When Odysseus meets Achilles during his visit to the Underworld, the ghost of Achilles tells the king of Ithaca that death is terrible. In fact, Achilles says, he would rather be a living, breathing, normal person than a famous but dead hero. 

This moment is intriguing because Achilles specifically chose a short but glorious life in favor of a long but unremarkable one. Getting what he wished for, Achilles became renowned as the greatest warrior who ever lived, but he also died on the battlefield at Troy. As such, it would appear that Achilles regrets his decision, and that he specifically regrets his decision to value fame and glory over all else. Thus, when Odysseus sees Achilles in the Underworld, the ghostly warrior seems to question the whole enterprise of yearning for a mythological reputation. This notion seems to undermine the whole point of epic poetry (which essentially celebrates the larger-than-life deeds of heroes), and so it serves as a surprisingly subversive philosophical point. Perhaps, Homer seems to suggest, it would be better to avoid idealizing the blustering heroes of The Iliad and The Odyssey, as the life of epic poetry is not as glamorous as it seems.