It isn't clear though how they finally did, or I don't remember it. What I remember is that a bunch of Wardens together took him down, but I don't believe it said just how they took him down. Actually I don't think they did, as I said a couple of posts ago, I think Evil Bob is actually Kemmler.
My tin hat theory!
What if Bob has been Kemmler all along? Bob is a spirit, can he be killed? Don't think so unless maybe Mab can do it. Is that why Bob fears Mab? Or is it because Mab knows who and what he is? Anyway, so the Wardens "kill" Kemmler, but they don't really because he retreats in his spirit form, or Bob. Bob is very useful so a Warden like Justin steals him for his own use. Justin was a Warden, he wasn't always evil, but what if having "Bob" in his possession corrupted him? Turning Justin warlock? "Bob" would know about star born, "Bob" would have plans for such children.. Monkey wrench into the plan, Harry Dresden. Harry kills Justin, takes the skull and names the spirit, "Bob." Just naming the spirit begins to transform him, also Harry orders him to forget the evil stuff he knew before Justin died. Thus it was until Harry needed information about Kemmler and ordered a reluctant Bob to call him up. Evil Bob emerged and nearly killed Harry, after that Bob was so horrified he cut himself off from his evil "memories" for good. Those memories became Evil Bob who we met in Ghost Story, or was it really Kemmler?
A lot of WOJ's about Bob would have to have been lies by Jim to cover up a plot twist for that to be the case, but then again, that is something he'll do if it's an important enough plot twist.
Bob is plenty destructible, though. Sunlight when he's out of the skull is a deadly danger to him. Same for fire.
Given Harry's experience of walking around as a naked soul where fire was still a danger to him, too, I think that was probably key to how the Council got Kemmler for good. There's a WOJ about the final execution involving a flamethrower - I think as the spirit comes out of the body, the fire gets that too.
Which, actually, also goes a long way toward an in-universe explanation for the witch hunts using burning at the stake. I wonder if it was an early version of the Stokerlypse, with someone in the know recommending the Inquisition a way to conduct their executions that would actually end pretty high-level warlocks.