Looking at how big the hydra is, Cutting her six heads off seemed like an impossible task. Cain could only think of a few drastic measures, risking a lot to just have a chance of killing it.
Alice could stop the hydra's regeneration by using [Cursed Decay] but that is not a thing he could let her do in front of all those people. It will work by making the wounds rot and preventing them from healing.
He could also use High-tier magic to blast it in one go but that would probably kill him. It will require the firepower of sixth or even seventh-tier magic because ho big the hydra is. Unlike the time when he healed Alice, he is now using attack magic which imposed more strains on the body.
Stale for a long time, and force the hydra to fight until it exhausts all of its stamina. Doing that might take more than a day, by that time the hydra would have already wreaked havoc.
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Would it have been better if he just summoned Sylph?