Drizzt 

D&D is itself an extension of mythology and sometimes it’s a good move for the GM to bring a proper legend into their game. Whether to have an epic NPC make an impact on the plot, slack a few jaws in awe, or just as a lark, this column is bringing you the greatest figures of mythology with statistics for Fifth Edition!...
Bestowed Invulnerability. Achilles mother Thetis dipped him into the River Styx in his infancy, turning his skin nigh-invulnerable. He is immune to sneak attack damage, ignores extra damage from critical hits, and has resistance to bludgeoning, piercing, and slashing damage. A creature targeting Achilles' singular point of vulnerability (his left heel) has a -10 penalty on its attack roll, but on a hit the attack deals normal damage (ignoring the immunities and resistances of this feature)...
It is always problematic when trying to adapt literary characters to the game, and with a mythological figure, it's especially so, since there is no single source to which one can appeal.
Let's lay out some basics, though:
The Greco-Roman sources for Achilles that survive include Homer (c. 700 BCE, reflecting an earlier oral tradition that preserves details from the Bronze Age) to tragedy (he's a character in Euripides' Iphigenia in Aulis, produced in 405 BCE) to Hellenistic works (including Apollonius' Argonautica, where he appears as a baby) to Roman works in Greek (Apollodorus' Library) and Latin (Ovid, Hyginus) that extend into the second century CE. That's 900+ years of history, plus ancient commentators on the lot, and not including lost works throughout that period but which are indirectly attested, that we refer to when we're talking about "the myth" or "the legend". Throughout that time, there is no obligation on any of these creators to adhere to what has gone before, and each will use the character in their own way for their own literary purposes. "The Myth" simply doesn't exist; there is only an ongoing accretion of detail some of which will agree with what's gone before, and some of which won't.
We can't know "the original story" (it predates literacy) and so if we want to speak at all meaningfully about this, we need to pick an author we like.
The OP mentions Homer and the Iliad, but if you're going with that, you find yourself quickly stuck.
Homer doesn't know about the invulnerability. In fact, that detail isn't attested until after the death of Alexander the Great, four centuries later. Some scholars guess it's an earlier tale, but "the legend" and "the myth" simply doesn't support it.
Though not invulnerable, he is able to fight a river and then kill Hector (Iliad 20-22). For Homer, he demonstrates speed ("swift-footed Achilles"), high constitution and strength (he is the single best hand-to-hand fighter at Troy, on either side; so 20 Strength and Constitution?).
In the Odyssey, he is the wisest person Odysseus encounters in the underworld, so we should give him at least a posthumous 18 wisdom.
Vase-painting (and lost tragedies about Palamedes) have him regularly playing tactical board games, which suggests Intelligence. Euripides in the fifth century plays up his Charisma. Etc.
In Homer, he uniquely uses his father's spear (which for some reason only he an use/lift). He doesn't use a bow or a sword (though there is a really good sword scene at the start of the movie Troy).
I understand the desire to stat up mythic figures, but (not to be too much of a pessimist) it's a mug's game, and you can justify almost any decision because the sources simply do not agree with one another.
The same will be true of other figures who are less well attested (Daedalus) or who developed over several hundred years (Lancelot, Robin Hood).
There is not, and cannot be, a right answer.
I don't think that's a thing. IF you want evidence of his wisdom in the Iliad, check his discussion with Priam in book 24. He provides the most meaningful description (within the poem) of how fate works, and how human and divine existence operates.[MENTION=23484]Kobold Stew[/MENTION] #14 So i did Forget that thing about him being wise in the odissy. Still i believe he achieves this wisdom post mortem.
In the Iliad Achilles is the least impulsive person of all the Greeks. Diomedes (book 5 [attacking the gods]) is impulsive. So is Patroclus (books 15-16 [not sticking to the plan, going to the walls]), and Odysseus (Odyssey 8 [throwing the discus], 9 [telling Polyphemus his name], 10 [spending time with Circe], 11 [stupid underworld boasts], 13 [accusing Athena of abandoning him]).In the iliad he is pictured very impulsive which speaks for low to average scores for int and wisdom. So i think i might correct my above stats to 12 in Int but leave wis at 10. Definitely he has high Charisma though.