No, it would not be correct with "for". Also, you should delete "would" and make it two sentences, thus: "I need your help with this assignment. Do you mind staying back for an hour?".
It sounds like asking someone to do the homework on the speaker's behalf.Can you get help for me(somebody) to do my homework.
Please note how to ask the question.I would need your help for this assignment.
Why [STRIKE]'for'[/STRIKE] is "for" not correct?