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FitFinlay provided a great argument, but remember that Knuckles can turn into Hyper Knuckles for a limited amount of time, which grants him invincibility and increases his considerable strength and speed. Knuckles has defeated giant robots that provide a ton of power before, and I don't see why he can't here.
You see, Juggernaut has a weak spot in the exposed parts on his face. Knuckles could turn Hyper, glide up to Juggernaut's face or other exposed area, and punch away at him into he's knocked out. That is how I see Knuckles winning - A lot of damage on a weak point in a short amount of time, much like how he defeats bosses in the games.