I wouldn't have killed it, just trapped it somehow in some way that's impossible for it to escape, so it's no longer a threat.
My preferred method of 'killing' a ghost would be to write it in such a way that the ghost is being tied to reality by some sort of unfinished business, that they simply can't move on until whatever is binding them to their old lives is finally put to rest and resolved. Though I don't think that really applies to the scenario the OP has in mind. Why are they hunting the ghost of the serial killer? Is he still able to interact with the real world and kill people whilst in corporeal form? Or can he possess the bodies of the living and make them commit acts of murder? I think a nice solution would be to trap the ghost rather than outright destroy it, as you say in the OP, you can't kill what's already dead. Perhaps you could write a finale where the heroes struggle to perform a ritual that binds the spirit of the ghost to an inanimate object, like a wooden ornament, a glass jar, a shoebox, or something. Would leave a nice little thread open for future tales too, where someone might discover the object and unknowingly set the killer free again. The thing is, the science of killing ghosts isn't really something that someone is going to call you out on because you didn't write it according to realism. So you literally can write absolutely anything you want.
Use modern physics like the LHC at CERN. Trap him in a particle accelerator and accelerate to the speed of light and whammo! Assume ghosts are energy or matter; it's not that important. Do enough research to sound educated about particle physics and I doubt more than three readers will be able to call BS.
Why kill it in the first place? ...second place, actually, because it/he/she died already, once, so this would be the second death, or whatever... Maybe everybody could get along in the end, like in "Beetlejuice"... ahhh, Beetlejuice.... As others said: what is your ghost, how do you define it in the context of your story? You decide on the rules, so you decide on how to end it.
Maybe you could raise up another ghost, one with a ghost weapon that could vanquish it for you? Then again if you called up one powerful enough to destroy the first one you might be right back where you started.
Hmmm... How do you kill something that is already dead? Forgive me for sounding facetious, but I would think that if you want to stop something from being dead... you need to reincarnate it... bring it back to life. Or you could trap it and render it harmless. My wife and I had a ghost in our house and we just sucked him up in the Dust-Buster!
Maybe shedding more light on how your antagonist came into existence could also provide a solution to your problem. Hope it helps.
Someone stronger than the ghost of a killer in the past? Well, you can't kill someone who is already dead. If it's a malignant spirit that causes demonic activities or harming someone in the process, you might need to include an exorcist priest and his laymen in your story to do the work.