Your starting match will be against Painwheel. While fetching the video for this guide, I realized that MF's storyline is actually pretty easy! I always spam QCF + HP > HPx2 (Quarter-circle foward plus High Punch, chained directly into two High Punches) for easy kills.
Your second fight is against Peacock. For the sake of keeping the descriptions short and sweet, just refer to the first fight Vs. Painwheel for the most effective disposal strategy.
Your third fight is up against Valentine. She doesn't do much once you have your combo going (y'know, the one from the first fight).
Your fourth fight is against Parasoul. Again, she doesn't fight back once you've got her pinned down.
Once in the Grand Cathedral, you're pitted against Valentine.....again. Except this time, she has Double with her for your first double battle. Again, Valentine won't do anything once pinned down. Use the combo from the first fight to take her out.
After Valentine is down, Double will come out immediately. Upon her arrival, you might take some damage. Don't fret though, you should just be able to shrug it off and start comboing her like the other girls you've fought in this story. Once Double is out