Typhon

Typhon (a.k.a. Typhoeus) (Τυφών in Ancient Greek) is the last child of Gaea and is also known as the "Storm Giant" or "Father of all Monsters." His wife is Echidna, and his father is the spirit of Tartarus. Especially hated by Aeolus, when Typhon is defeated thousands of Venti are realeased, giving the wind god a tough job. He is the most powerful foe and the biggest threat to Olympus.

History
Thousands of years ago, after the First Olympian War, Gaea was enraged at the defeat of the Titans her children and of how they were locked away in Tartarus. She attempted revenge by sending her last and most powerful child, the great monster Typhon to destroy the gods. Typhon alone is the greatest foe the gods ever faced, even mightier than the Titans themselves.

Having never anticipated such a rival, the gods were quickly forced on the defensive and eventually went into hiding. Athena however stood her ground and convinced Zeus to fight by calling him a coward. This convinced Zeus and he went into battle with his lightning. Zeus struck Typhon square in the chest with the Master Bolt at point blank range, greatly weakening him. The gods were then able to trap him under Mount Etna, where his raw power itself causes lava to ignite from the mountain top in the form of a volcano. After the defeat of her most powerful child, Gaea admitted defeat and fell back to sleep and allowed the gods to rule Olympus without interference.

Western Civilization
When the gods moved and followed the center of power of Western Civilization, Typhon was trapped in Mount Saint Helens. Like in Mount Etna, his raw power ignites lava from the mountain top. Though he was successfully imprisoned for thousands of years, his prison could not hold him forever. During his efforts to kill a gang of Telekhines in The Battle of the Labyrinth, Percy was forced to call on all of his power to escape Mount Saint Helens. It was this that weakened the seal on Typhon's prison and awakened the Father of all Monsters. It was soon that Typhon would rise again to finish what he started at the First Olympian War; destroy the gods.

The Titan's Curse
When hypothesizing about the identity of the "bane of Olympus", Chiron suggests it might be Typhon.

The Battle of the Labyrinth
Typhon is mentioned by Hephaestus. Later, Percy causes an explosion in Mount Saint Helens made Typhon stir in his sleep.

The Last Olympian
Typhon escapes in a catastrophic explosion of Mount Saint Helens. Following his escape, Typhon heads to New York. Using the Mist, Typhon is able to conceal his true form from the mortals and appears as a freak storm. The Gods, at the very least Artemis, Apollo, Athena, Hermes, Ares, Dionysus, Hephaestus and Zeus are the only ones named, are unable defeat him as Poseidon is occupied defending his undersea kingdom and Hades, Demeter and Persephone refuse to fight. Not even Zeus' Master bolt, the most powerful weapon ever created, could stop him (Percy, through a projection on Olympus, saw that he merely stumbled backwards before continuing his way towards Olympus). He also incapacitated Dionysus and Hephaestus along the way, knocking Dionysus into a mountain range and causes Hephaestus to create a new lake. While the Gods are busy fending off Typhon, the Titans made their way to Olympus, which was being defended by demigods.

Percy prays to his dad and asks him to leave his kingdom and come to help the Olympians defeat Typhon. His father agrees and reluctantly leaves his kingdom to assist the gods. When Typhon steps into the Hudson River, the call of the ocean is heard and Poseidon rides into battle along with Tyson (who was 30 feet tall) and his brethren, the Cyclopes. They chain him down, and Poseidon opens a tunnel to Tartarus, and casts Typhon down. Once Typhon was defeated, a wave of venti (storm spirits) were born.

The Lost Hero
Jason Grace, Piper McLean, and Leo Valdez went to Boreas to help them in their quest to save Hera. As he explained the release of the storm spirits, he showed them a video image of the gods defeating Typhon with Poseidon's help.

Appearance
Typhon's true appearance is unknown and perhaps impossible for a mortal or even a demigod to view without going insane. Typhon can possibly have a Divine Form as he is the son of two gods (Gaea and Tartarus). Through the mist, Typhon appears to mortals as a massive freak storm and tornadoes that tear apart everything in their path. To demigods (who are immune or highly resistant to the Mist) he appears as a large shadowy figure compose of dark clouds. If a demigod or mortal looks at him too long they risk going insane from trying to comprehend what they are looking at. Based on comments, he has some sort of structure to serve as legs (possibly serpents according to myth) and claw-like structures or hands to attack his enemies. Percy also tells that he could not identify the monsters face because it changed every second to even more horrifying monster then the previous one.

Abilities
Typhon is one of the most powerful beings in all of Greek mythology. He rivals the combined powers of most, if not all the major Olympian gods. The full extent of his power is unknown. He can create storms of tremendous power including tornadoes, storms and possibly hurricanes. He has unbelievable physical strength and durability surpassing that of any individual god. He was able to fight most of the major gods to a near standstill, withstanding all of their attacks throughout including multiple attacks from the Master Bolt, numerous lesser thunderbolts, the arrows of Apollo and Artemis, and numerous other attacks. He was strong enough to hit Hephaestus with enough force to create a new lake and smash Dionysus deep into a mountain. He presumably has the standard powers of a god, but surpassing that of any other.

Trivia

 * Typhon is often known as the most powerful monster of all, but Porphyrion has claimed that he and his fellow giants are most powerful children of Gaea which raises questions over who is the more powerful being.