In Russian we have idiom/saying "To shoot out of cannon into sparrows" (literal translation) which is used to convey an idea of applying too drastic measures to small problems. I believe there should be some native-English equivalents to this saying. Can you share if there are any?
Overkill is originally a military analysis term from the Cold War, referring to the fact that the belligerents each had far more nuclear weapons than they would need to completely destroy the other. These days it's generally used metaphorically to mean precisely the sort of excessive effort or excessive means you talk of.
Bring a gun to a knife-fight is another that comes from combat originally.
Two idioms would be:
- To crack a nut with a sledgehammer.
- To break a (butter)fly on the wheel.
The wheel in question being a device for capital punishment of humans. So using it on a tiny fly would, quite literally, be overkill and it is also not clear if you would actually hit the fly at all or if it would be able to get away swiftly — a connotation it has in common with the Russian idiom you are translating.
As AJ Henderson notes in the comments, there are several common variants of "attacking some small creatures with a large and unwieldy weapon" in use, and I doubt most English-speakers would bat an eye at "shooting sparrows with a cannon."
That said, in my experience, flies do seem to be a more common target in English than sparrows, while the most popular weapons seem to be either cannons or, for a more personal type of combat, sledgehammers. So I'd most likely go for either:
"shooting flies with a cannon," or
"swatting flies with a sledgehammer."
But if you'd prefer to target sparrows instead of flies, please do. Such little departures from the most heavily trodden path will simply give your writing that little bit of extra flavor.
You could always nuke the entire site.