Your situation is very real. When you come out to work next
time, you can often find similar people in your workplace.
I think you don't have to approach your supervisor at all. Just
continue to do your part and get into the good books of your
supervisor, SHOW him by presenting results, ask him questions
pertaining to the experiments. He will see who is working. You 2
don't share the same grade.
Time wise of course need to confront your fyp mate lah, compliment
her on her report skills. Then ask her to help churn out the report
as you prepare experimental results. If she doesn't want to, then
prepare your own. Keep it a secret until she panick just before the
deadline.
Things will work out fine. 
