Hydra are hard to beat once established. I have had a lot of trouble with them because I feed freshly hatched brine shrimp, which they love.
In small numbers, they can be carefully shot with a syringe of Hydrogen peroxide. A direct hit with a tiny bit will do them in. But you have to identify the food they are multiplying on. In many tanks, they are just around and never become an issue. Something triggers an 'outbreak'.
There are a lot of species and not a lot of them do serious damage with their stingers.
I have had them doing just fine in guppy tanks. I used to breed wild sourced guppies from a Trinidadian friend, and since they were smaller than linebred guppies they got brine shrimp. Their tanks got Hydra flare ups and they wouldn't eat them even if given no other options.
You are in the US, so you may be able to get chemical products that'll kill them. Any helpful US members who can suggest something?