I've never paid any interest in Juggy before, mostly just seeing him as big guy with funny hat, but this whole concept of unstoppable/invulnerable intrigues me.
If he's invulnerable to physical harm then sonics shouldn't affect him, seeings as sound is basically shock waves and travel from atom to atom. Adapting the frequency you can shatter glass and affect your environment in a physical way. There is no magic behind it.
From what I can understand it's stated that Juggy's brain is vulnerable, but not the brain itself. If his brain in itself would be vulnerable you should be able to take him down with say a fencing sword if you managed to hit his ear canal. Rather nasty, but down he goes. But if he's invulnerable to physical arm he might just sense a slightly tickling. "Juggy sense, tingling".
But if the brain is susceptible to outer influence, can he be hypnotized? I can't see him being able to fend himself of that, unless he starts wearing some kind of anti shades.