[B0rsuk]

Increasing HP would be redundant, because we already have 'burning out' mechanic. It's called Fatigue. Fatigued enemies are easier to hit, and after certain point can no longer fight.

2. Achilles' near invulnerability came from his mother Thetis dipping most of his body (except the notorious Achilles' "Heel") in the River Styx. One could say that that is an equivalent of his natural armor or "protection" but it could also said to represent his natural hardiness or constitution or--gasp!--HP. To insist on Achilles' near-invulnerability solely as a category of "protection" may be to try to interpret everything according to your convenience

Translation: I like the legend about Achilles, but not that part about magical origins of his power. The part about hero is right, the part about magical protection is wrong. Because I say so.

Some quotes from wikipedia:

When Achilles was born, Thetis tried to make him immortal by dipping him in the river Styx. However, she forgot to wet the heel she held him by, leaving him vulnerable at that spot

In another version of the story, Thetis anointed the boy in ambrosia and put him on top of a fire to burn away the mortal parts of his body. She was interrupted by Peleus and abandoned both father and son in a rage.

Homer does not make reference to this invulnerability in the Iliad. To the contrary, he mentions Achilles being wounded. (In Book 21 the Paeonian hero Asteropaeus, son of Pelegon, challenged Achilles by the river Scamander. He cast two spears at once, one grazed Achilles' elbow, "drawing a spurt of blood.")

So, in two first quotes Achilles is said to be nearly immortal. Styx is no ordinary river, and ambrosia is food of the gods. There's also mention of burning away mortal parts of his body.
We see Homer didn't mention Achilles' invulnerability, and there's one case of him being wounded. His elbow was grazed by a thrown spear. You don't easily die from a hit to elbow, much less a graze. If anything, it could be said that Thetis' Blessing gave him heroic defence/reflexes. Because the worst wound he received (before the final one) was grazed elbow.
Doesn't sound like he had a lot of hps, does it ? It's either Protection, or reflexes (Defence) if you listen to Homer.

As predicted by Hector with his dying breath, Achilles was thereafter killed by Paris — either by an arrow to the heel, or in an older version by a knife to the back while visiting Polyxena, a princess of Troy. In some versions, the god Apollo guided Paris' arrow.

Both versions conspicuously deny the killer any sort of valor owing to the common conception that Paris was a coward and not the man his brother Hector was, and Achilles remains undefeated on the battlefield.

So in one version he was hit in the heel and it was enough to kill him. In another(never saw this one), he was killed (one shot !!!) by knife in the back.
Even if you assume totally realistic point of view and support the idea that Achilles' tendon was crippled, it seems to imply that it made him lose his Defence and dodging ability.
I'd also like to note that Greeks considered all ranged weapons, especially bows, cowardly. Their military was really centered around heavy infantry. Most probably because bows tend to ignore target's Defence, and you can't show your skill in melee combat.
Either way, Achilles died from a single blow.

As to Herakles, the only instance of him being wounded I remember was a crab that cut into his feet while he was wrestling with a legendary monster, don't remember which one.

Achilles' armor was the object of a feud between Odysseus and Telamonian Ajax (Achilles' older cousin). They competed for it by giving speeches on why they were the bravest after Achilles and the most deserving to receive it. Odysseus won. Ajax went mad with grief and vowed to kill his comrades; he started killing cattle or sheep, thinking in his madness that they were Greek soldiers. He then killed himself.

Because there's mention of Odysseus, I assume it was Homer who wrote this. It seems to imply that Achilles' power at least partially came from his armor - or so the two Greeks believed. What it doesn't do is support the HP hypothesis.

Let's face it, HP is a crude, old oversimplification in an old and flawed system like D&D. And if I remember correctly, the way AC works in D&D comes from pen&paper Mechwarrior games. (Just to support the idea that D&D). D&D says futuristic giant walking robots have more in common with ancient/medieval combat than history. That's guilty enough for me. And let's not forget D&D was optimised for humans - that is, GM had to be able to calculate everything quickly without help of computers.