Greek mythology has no chronology in our sense.
Hercules killed the hydra, not odysseus
The Lernean Hydra is killed by Heracles in his second of twelve labors. However why the Hydra is killed is never fully explained.
The nine headed creature was a hydra
the hydra
keep jumping on its heads and try not to get hit or else one of the heads you already killed wakes up
The Hydra
Hydra
6 headed monster
Hercules/Heracles killed the Nemean Lion and the Hydra.
The Hydra but it is interesting to note that it was the Hydra that did Hercules in at the end.
The Greek monster with nine heads is called the Hydra.
It was a hydra.