After selecting Filia from the list of characters, you will be placed in Filia's story mode. Again, I will not be going over the story, that is for you to learn on your own.
Your first fight will be against Parasoul. I usually do LP > MP > HK (Low Punnch to Middle Punch to High Kick) for results, but you can always just spam buttons. Stay away from her Napalm Shots.
Directly after fighting Parasoul, you will be up against Cerebella. Again, a fairly easy fight. Just button mash or use the combo I introduced earlier.
After the small bit of story, you will be up against Painwheel. Again, easy match. Try to use your level 1 blockbuster as much as you can. The input for it is QCB + KK (Quarter-circle back plus any two kick inputs).
Your fourth fight will be up against Ms. Fortune. Usually when I fight her, she doesn't even get to attack me. Mash HK (High Kick) to knock her down, should be enough to win.
Your fifth fight is a double battle against both Double and Valentine. Double is a priority target. Unless you're playing on Sleepwalk difficulty, Double will always try to combo you while you can't attack her. So just use HK (High Kick) to knock her down and then hit her with all you have.
Double may swap to Valentine at any time, or Valenitine will fight when Double dies, so just be aware of when she swaps. Valentine, again, will combo will. Hard. So just knock her down with HK (High Kick) and then unleash your fury.
After the story arch, you will arrive at the bottom of the Grand Cathedral, against the final boss: Marie. Click "Next Page" for some tips on fighting her as Filia.