Your first fight is up against Filia. Sadly, this is yet another character with a broken and spammable attack. In all of Cerebella's battles, you can just strike first with w.HP (Walking High Punch), get close, and then spam HP (High Punch, do not try this while moving) to defeat her.
Your second fight is up against Ms. Fortune. Same combo as first match, and the combo will be the same for any other fight.
The third person you fight is Parasoul. Yet again, you can spam HP to win. Or, just mix it up and fight her your own way, makes things more interesting.
Your fourth fight is up against Valentine and, well, Cerebella. Two choices here; Spam HP or try your own combos. Either way, they'll both go down pretty fast since Cerebella is a really strong character.
Your fifth fight is against Double. Unlike any other character, you fight Double alone (usually, she's paired with Valentine). Yet again, spam HP for victory.
Once that's all done, you'll move on to meet the Skullgirl; Marie. Go ahead and hit "Next Page" to see Cerebella's guide for fighting Marie.
Like Parasoul's fight with Marie, this one will be a doozy. Attack her head on with w.HP (Walking High Punch) to start off.
Use QCF + HP (Quarter-circle foward plus High Punch) to charge towards Marie and do a lot of damage. Just spam this move until Marie is in her third form.
Here's a picture of the combo still being used on Marie in her second form.
When Marie's in her third form, you can spam j.HK (Jumping High Kick) to lower her health quickly. She should be knocked out after about 3-4 times.
After all that's done, Marie is now defeated, congrats. Click "Next Page" to move on to the final story; Painwheel.