This simple fact is Batman is only a man who happens to be a scientist, detective, and martial arts expert. The key here is that he has no superhuman powers.
So clearly, Spiderman can beat him up.
From the Marvel Universe website:
Spider-Man possesses superhuman strength, reflexes and equilibrium; the ability to cling to most surfaces; and a sixth sense that warns him of impending danger.
Batman is pretty tough but he is clearly outmanned here. The answer is clear:
Spiderman can beat up Batman. Spiderman has powers. Batman does not.
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