Hydra

The Hydra was a vicious monster.

'The Sea of Monsters
When Percy sent Tyson to look for doughnut store, so he could talk to Annabeth, Tyson went out and came upon a Monster Doughnut store. Tyson, being a monster was somehow able to summon the outlet bringing the Hydra with it. It was large and lizardlike, with a long neck and several heads. It had many rows of razor-sharp teeth, its hands were clawed, had a tail, and spat acid. According to Annabeth, another Monster Doughnut shop popped up every time it grew another head. Percy initially tried to defeat it by slicing off its heads, but succeeded only in making more. Percy and Annabeth were saved by Clarisse when the Hydra's heads were lit aflame and burnt off by cannon fire from the CSS Birmingham.

Spoil of War
In the attic of The Big House in Camp Half Blood, the original Hydra head was left as a spoil of war. This incarnation of the monster was defeated in Woodstock, New York in 1969.

Greek Mythology
In Greek myths and legends the Hydra was a vicious monster with multiple snake heads. When one head was decapitated, two more snake-heads would grow in its place. Hercules eventually defeated the Hydra, by having one of his soldiers give him a torch burning every neck, before the heads reproduced, then caused a rock slide, and left the immortal head.

The Lightning Thief
The Hydra is featured in The Lightning Thief. Percy Jackson, Annabeth Chase, and Grover Underwood encounter the Hydra in the form of 5 Security Guards at the replica of the Parthenon in Tennessee, after Percy Jackson takes Persephone's Pearl (originally Poseidon's) from the Athena's. When Percy ripped Hydra's Head with Riptide (his magical and trustworthy celestial bronze sword) two more appear. Grover managed to defeat the Hydra using Medusa's head - a possible reference to some accounts of Perseus slaying Cetus. That scene replaced Percy's encounter with Echidna and Chimera at the St. Louis Arch from the book; it should be noted that the Hydra is depicted as breathing fire in the film instead of acid, a possible reference to the Chimera's flame breath. After Percy cuts his middle head, two of the Hydra's head breathe fire.