I take it you are referring to the section where Achilles discusses the prophecy that his mother, Thetis, made about his life. In this section we see the irony of the life of the famed warrior Achilles. He is renowned for his strength and valour, but according to his mother, he has a choice to make. He can either stay fighting against Troy, which will ensure his death. However, ironically, this death will mean that his "glory will never die." The alternative is to return home, leaving the battle, and have a long life but one that will be ultimately forgotten as his "fame will die" instead of his body. It is ironic that Achilles can only choose between eternal fame or a long life, and cannot have both.
However, we can also detect another note of irony in his counsel to his fellow soldiers to return home, because of his belief that Zeus will prevent any successful attack:
You’ll not attain your goal,
steep Ilion, because far-seeing Zeus
shields that city with his hand.
Of course, we know that this is not the case and that Zeus will allow Troy to fall and give the Greeks victory.