What can she do to beat him? He built her weapons and know how they work. She's not getting the jump on him with it. He also took on luffy ( with prep). He has better speed feats and durability than her.
True, but honesly Luffy beat him easily. Nami has actually managed to take down stronger opponents than Usopp on the relatively rare occasion they get 1 on 1 battles. Her weapon is better than his too, even though he made them. In short, while I think Nami has stronger weapons, Usopp can beat her due to his own knowledge of them.
That is true. With no knowledge Usopp can't do much. He couldn't avoid the lightning and her mirage ability would make tagging her unlikely. Even with knowledge he faces the same problems. Actually Nami should beat him either way.
Usopp has the advantage in all around stats, but Nami's weapon and her proficiency using it would probably be enough to beat him more times than not, and even if Usopp did manage to get the upper hand or win, he'll regret it as soon as Sanji finds out.