Hydra constellation is remembered through Hydra story of Hercules. In this story Hercules could not kill hydra, he merely placed a huge stone over it's head. Note the Corvus constellation which looks like the stone placed over the head of Hydra constellation.
Krishna also did not kill Hydra, he merely directed him simply move away and not to harm the people of Brindavan. See, the picture of Krishna standing over snake kalingarayan, it is merely a modified story of Hercules fighting Hydra.All these events did not happen in earth, all these fightings and killing happened in Heavens (sky). Krishna simply moved from one constellation to other killing those heavenly animals.
(Picture from Wikipedia)