I believe that a water bear could defeat a hydra any day. The water bear could win by forcing the hydra to a desert and letting it getting dehydrated because a water bear can go without food or water for ten day. it can also survive in extreme conditions such as from just above absolute zero degrees Kelvin to well above the boiling point of water. it can survive in pressure six times as much as humans. They can also survive levels of radiation that are hundreds of times higher than humans as well as remain alive in space. with how the water bear can do I do not believe that the hydra can best it.
I would just like to open out with how could the Water Bear(or Tardigrade) drive a hydra out of the water when the largest recorded size of a water bear is 1.3 MILLIMETERS! Where as the lernaean hydra from Greek mythology was said to be larger than a man with more heads than one could paint. You may say that because of its size it would not be hit but it would only be a matter of time before the hydra spit some poison and killed it. Also he Hydra emits a poisonous fumes since this is a creature created by the goddess Hera would probably be lethal to any and all creatures.
The Tardigrade could infect the hydra and would cause death. The water bear probably wouldn't be harmed by the fumes as it is immune to so much already. If the water bear got on the hydras skin then the hydra would not risk hitting itself with the poison. Since fire is what killed the hydra the water bear could get the hydra on fire and still survive the blistering heat.
Once again how in the world could such a microscopic organism such as the Tardigrade/Water Bear even drive the hydra anywhere? Also the Water Bear can only survive in temperatures as much as 151 degrees Celsius which is only 303.8 degrees Fahrenheit... for a few minutes! Fire burns at around 1950 degrees Celsius which is 3542 degrees Fahrenheit, more than 10 times more than a Water Bear can handle. And I'm pretty sure that since the hydra was brought to life to kill Hercules I'm pretty sure its skin is more than a millimeter deep and on no accounts any where have I found that a Tardigrade carries poison at all. That the Lernaean hydra was killed by fire bands placed around its throat after and only after the incredibly strong Hercules chopped a head off and then using a golden mythical sword, probably a couple thousand times larger than the Tardigrade.