Once you've selected Double from the character list, you will be up against your first opponent: Filia. To be honest, I don't play or like Double enough as a character to know much about her. Normall I just end up spamming MKx2 (Middle kick two times rapidly) for maximum results. Also, make sure to use your level 1 blockbuster when you can. The input for it is QCB + PP (Quarter-circle back plus any two punch inputs).
Your second fight is against Cerebella. Again, MKx2 is a viable combo. Just do your best to keep pressure on her and avoid Cerebella's grapple moves (she has a lot).
Your third fight will be against Peacock. Peacock's AI is programmed to keep you as far away as possible. Use your level 1 blockbuster (Again, QCB + PP) to get close to Peacock and make sure she can't get too far away from you.
The fourth girl you fight against will be Ms. Fortune. You can either confront her up close and keep up the pressure so she can't attack, or wait for her to toss her head and then attack that. It's really just up to you on this one.
Your fifth fight is against Painwheel. Painwheel isn't very fast, but she hits very hard. Get close and spam buttons so she can't attack you.
Your sixth (and final) fight is against Valentine. Again, just do your best to get close to her and make sure she can't attack you, she has a powerful mixture of easy-comboing close-range attacks and annoying long-range attacks.
Once that ordeal is over, you'll be headed down to the Grand Cathedral basement to find the Skullgirl once and for all. Click "Next Page" for Double's guide to beating the Skullgirl; Marie.