I've heard that the name Achilles can translate to something like "the grief of the people," which is pretty much the saddest thing in the world. It is a lovely name, and Achilles is a fantastic figure (albeit flawed), but I'd say be careful about this as a first name, as it really can sound pretentious.
From "achos" (pain) and "laos" (the people) - pain of the people. When he was fighting in the Trojan War, he was the pain of the people for the Trojans, and when he was not fighting (like when he was mad at Agamemnon, or before he arrived at Troy), he was the pain of the people for the Greeks. He was also the pain of the people for his mother, who knew he would die young and that upset her. By the way, he was not suckled as a baby when he was with the centaur Chiron.
The name αχιλλευς comes from the Greek word αχλύς which is a weather phenomenon mainly seen in Greek rivers, lakes and the sea. It is similar to myst. The word αχλυς (achlys) derives from the morpheme αχ (ach) which is present in words representing names of big Greek rivers. e.g. Αχ-ελώος, Ιν-αχ-ος Αχ-ερων. Achille's chariot raised clouds of dust (resembling achlys) and thus took his name that reflected this property.
Translates as "without lips". Appolodorus suggests it may be because he was never suckled as a baby (!?). Could also imply Achilles is the name of an ancient oracular hero (hint: they keep the head in the shrine, over time the skin shrinks away...)
Like it was already mentioned, Αχιλλεύς (a-kil-LEFS) has to do with άχος (A-chos) - "pain", and the word "λύειν" (LI-in) - "to untie". "The One Untying the Pain" - possibly connected to healing capabilities.
It is a lovely name, and Achilles is a fantastic figure (albeit flawed), but I'd say be careful about this as a first name, as it really can sound pretentious.