As with Nalcon and Bustanor, you can use Breakaron to strike immediately and prevent him from generating webs and spiders.
With Breakron, you don't have to worry about aiming or distance. You don't even have to be facing the enemy, it will still connect.
While it can't be launched as fast as Bustanor, it still does an excellent job of rendering Spider powerless. As you can see he just walks towards you, and sometimes runs. That's the only thing to watch out for, so you'll need to reposition when he gets close.
Spider doesn't go to the ceiling once in this video, due to Breakaron being so slow that he has time to make his approach while I charge another. It's only rapid, consecutive hits that trigger that response.
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"I never asked to be born..." - Spider