Maybe The Guyver? I haven't seen it so I can't comment on the specifics of your memory but it was available on VHS at the time, featured a lot of biological monsters, and has a similar enough name to GitS that it could be misplaced in a foggy memory.
Though Akira does have a dude that transforms into what would qualify as a "giant monster", and while he doesn't attack a city he does end up destroying a large stadium. So even though there's no real "head in a jar" Akira might still fit. Also, regardless of whether its what you're looking for, you should still watch Akira. Just know that it's weird and you have to pay attention to what's going on or it won't make a lick of sense. It's not a "watch it and fiddle on your phone" kind of movie.