Curse of Achilles

The Curse of Achilles is a power and a curse that a person can acquire when they bathe in the River Styx.

Description
The curse is named after Achilles, the Ancient Greek hero, who was famous for his invulnerability. When one bathes in the River Styx, they will be granted the power to remain uninjured by any means. They must get their parent's blessing, however, before bathing in the river or it would kill whoever entered its' shores.

When one bathes in it, the person must envision one thing that ties them to the living. They also must imagine a single spot on their body that will be vulnerable and a rope tying them to the mortal plane. If they do not do this they will turn into ash and be forever lost in the River Styx. Though not proven, the thing a person usually envisions is often someone close. An example of this is when Luke bathes in the Styx, he envisioned Annabeth, the girl he loves.

Exposure to the water of the Tiber negates the curse permanently, because it is a Greek blessing/curse that could not be retained in territory belonging to the Romans (i.e. Camp Jupiter), the enemies of the Greeks, according to Juno.

Abilities
Anyone who bears the Curse of Achilles is nearly invulnerable, except in one weak point. They also get highly increased strength, speed, agility, reflexes, endurance, and fighting skills, also linking to their abilities, making it less tiresome to use immense powers. Percy was powerful enough to defeat Hades, Hyperion, a hundred skeletal warriors created by Hades, and a fraction of the Titan army equivalent to hundreds of monsters.

Weakness
The most obvious weakness is the mortal spot the person chooses, as it remains the only place that can be injured. If this spot is even slightly injured, the person will die immediately.

The less obvious weakness is a secondary function - in addition to gaining invulnerability, someone with the Curse of Achilles also gains extreme physical powers - heightened strength and reflexes - and a body that almost automatically fights. However, this places an enormous amount of stress on the body, requiring a warrior under the curse to be careful not to over-exert himself, which happens more quickly than before. Chiron said that Achilles himself took about twenty naps a day—it sometimes seemed that when Achilles wasn't fighting, he was either sleeping or eating. This means someone under the curse will tire fighting quicker than someone who isn't; meaning that if a person with the Curse of Achilles is attacked by a large enough army they can be overwhelmed or become too exhausted to fight. It is also mentioned that a person under the curse will have certain emotions or behaviors enhanced, normally having to do with their fatal flaw. One major weakness is that while you are immune to injury you can still be killed by other means, as your body is still mortal:
 * Dehydration
 * Asphyxiation (e.g. drowning, choking)
 * Diseases (heart attack, strokes, cancer,etc.)
 * Electrocution (during The Last Olympian, the river gods proclaim they can kill Percy Jackson with electric power cords)
 * Burning (during  The Last Olympian, when Kronos was trying to get his scythe he was burned by Hestia)
 * God's true form (obvious as the bearer is Invulnerable not Immortal so a god's divine form will still kill them)
 * God's wrath (while a bearer is still invulnerable, a god can still kill them with a snap of a finger as in The Last Olympian, Percy was afraid of bringing the entire fighting force to Mt. Olympus, afraid that the god's will be angry and "getting blasted to bits", and since god's are capable of killing mortal's with a thought this is very probable.)
 * Starvation
 * Poison
 * Exhaustion (Chiron mentioned that Achillies had to sleep "twenty times" a day, so if the Bearer of the Curse is constantly fighting for too long, than they can burn themselves out.)

As a Greek blessing, according to Juno, it has to be removed when entering Roman territory, specifically the Tiber River.

Trivia

 * When Percy was trying to pick his Achilles' heel, he said he didn't want to pick an embarrassing spot like his armpit. Later, when Luke asks for Annabeth's knife so he can kill himself, his Achilles' heel is under his left armpit. However, Percy says this was a good idea.
 * Apparently while being invulnerable, the bearer can still feel pain to a certain extent. An example includes when Percy was fighting the giant Cacus, and was very disoriented after being hit into a wall, almost knocking him out. Another time, Percy cried in pain when jumping onto Blackjack. Also Kronos, despite having Luke bathe in River Styx, was still burned by Hestia when he tried to grab his scythe.
 * The curse can apparently be removed when entering certain magical places connected to Rome, as the curse is a Greek blessing. One of these places is the Tiber River at Camp Jupiter, which has the ability to wash the curse away.
 * Your Achilles tendon is named after Achilles, due to it being close to the heel.
 * A common quote is someone's 'Achilles Heel,' which is someones weakness, named after Achilles because of  his weak heel.
 * All the known bearers of the curse in both the series and mythology were male. No female has been known to bear the curse.