Much like the mythical creature, the Hydra seem to multiply in numbers when defeated. Although they appear to be individual entities, it turns out they are disjointed parts of a collective creature.
According to information gathered by the United Nations global defense force Vanguard, the Hydra was created by the Rikti to guard their underground bases during the First Rikti Invasion of 2002. However, this is not a creature from the Rikti Universe. Rather, it is a creation from the native biological material in the sewers of Paragon City.
The simple creatures have an equally simple command: "Protect." They don't know what to protect or whom to protect it from. So they protect their territory from everything.
The Hydra have various stages of development, from simple tentacles to small "spawn" drones to a powerful creature dubbed the Kracken. But they all from one central creature that was created by the Rikti. A "mother" Hydra that senses all and gives them the simple command to "protect".
Originally infesting the sewers, the Hydra have since expanded to Perez Park due to substandard sewer lines in the area. It is because of them that Perez Park is deemed a Hazard Zone and why people are told to enter that area at their own risk.
(Check out their entry in Paragon Wiki for more information.)