According to myth, Achilles was dipped in the river Styx to make him immortal. His mother held him by the heel, however, leaving it vulnerable. Paris killed him in the Trojan War by hitting him in the heel with an arrow.
Robert Plant wrote the lyrics about his travels throughout Morocco, Greece, and Spain. The music was inspired by Flamenco and Moroccan traditions. The lyrics were inspired not only by the travels but also by some of the poetry Robert was reading at the time, which includes William Blake. "Albion remains/sleeping now to rise again" is a reference to Blake's engraving The Dance Of Albion. The following is an excerpt from the poem that goes with the song:
Albion rose from where he labour'd at the Mill with Slaves.
Giving himself for the Nations he danc'd the dance of Eternal Death.
The references to the Atlas mountains, "The mighty arms of Atlas hold the heavens from the Earth," are simply a clever double-meaning to imply the Atlas mountains in a physical sense seeming to hold up the sky, as well as the reference to the titan Atlas and his task to hold the world on his shoulders. (thanks, Mark - Phila, PA, for above 2)
Robert Plant and his wife were in a car crash while on holiday in Greece which broke Plant's ankle. Instead of touring the US, Plant and Jimmy Page wrote material for Presence, then recorded it at Musicland Studios in Munich, Germany with Plant in a wheelchair. Plant got so excited while recording this that he fell and re-injured his ankle, similarly to the song's namesake, Achilles. The title was both an acknowledgment of Plant's broken ankle as well as to the mystic location in the Atlas Mountains of Morocco which inspired the lyrics. (thanks, Nick - Warwick, RI)
Jimmy Page overdubbed 6 guitar tracks to create a huge sound. In a 2007 interview with Rolling Stone magazine, Jimmy Page was asked about his memories of how he overdubbed the guitars in the studio: "It was done in one evening, the whole of the arrangement. To be honest with you, the other guys didn't know: 'Has he gone mad? Does he know what he's doing?' But at the end of it, the picture became clear. It was like a little vignette, every time something comes around."
Page takes particular pride in this track. He told Guitar Player magazine in 1977: "Presence and my control over all the contributing factors to that LP – the fact that it was done in three weeks, and all the rest of it – is so good for me. It was just good for everything really, even though it was a very anxious point, and the anxiety shows, group-wise – you know, 'Is Robert going to walk again from his auto accident in Greece?' and all this sort of thing. But I guess the solo in 'Achilles' Last Stand' on Presence is in the same tradition as the solo from 'Stairway to Heaven' on the fourth LP. It is on that level to me."
Led Zeppelin played this at the remainder of their live shows.
This is one of the longest Led Zeppelin songs. It runs 10:26.