Can a Bristling Hydra activate Hexproof when an instant is cast?
Bristling Hydra is a bit tricky, because it has a triggered ability for when it enters the battlefield, that gives you energy. Making it hexproof also costs energy. If you had no energy before summoning it, your opponent could kill it in response to the "Enters the battlefield" trigger, and you wouldn't have the energy to activate its ability and make it hexproof in response.

However, if you had gotten energy from a different source earlier, you could activate its ability to make it hexproof in response.

(Also, if your opponent waited for the ETB trigger to resolve and give you energy, THEN cast a spell to kill it, you'd be able to pay energy to make it hexproof in response, although it seems unlikely that they would do that, seeing as it's a pretty bad play).