The Setup
First off, you must be on default settings.
Next select "Story Mode" from the menu and choose your characters.
You will fight 6 matches with 12 random opponents. They don't repeat, but they include the characters you chose. During the 6 matches you must meet these criteria:
- Connect at least 6 D-Assaults (AKA Double Assaults). They are performed by doing Quarter-circle Forward +
(QCF is
is your opponent is on the right side and 

if they're on the left) - You must not win by a timeout
- You must win with your team's average health above 50%
Once you finish your sixth match, a cutscene will play depending on which boss you get.
Goodman is a really cheap with his attacks. You will want to die the first time and then hit

at the continue screen. It will then give you a list of debuffs to apply to your opponent. Select "1/4 Opponent Life" and Goodman will start will 1/4 of his health. You can continue as much as you'd like once you get to Goodman.
My Experience
Go to "Practice" from the menu and choose Yuki and Ai (the two in the top middle) and then two random fighters. I then went to "Command", "Edit", deleted (DEL) everything in there and then inputted D, FD, F, SP (D is down, and F is forward). Go to "END", "EXIT", and select "YES" when asked "COMMAND CHANGE?" Then change "EXIT GAME" to "YES" and press

.
Then select "Story Mode" and choose Yuki and Ai and always started with Yuki as the 1st Player. I would then spam

which would play the command we made. The move sends a projectile forwards. If the enemy got to close, I would try and chase then off with Quarter-circle Back (opposite of QCF) +

or try landing a D-Assault. I would switch to Ai (QCB +

) to let Yuki regenerate health (red health can be regenerated) and then switched back.
When I got to Goodman, I applied the 1/4 health debuff and then used Yuki's QCB +

to close the gap and then QCB +

when I was close. When Yuki was low health, I would switch to Ai and then run up to Goodman and spam

+

and

+

until Ai had no health left. Then I would try Yuki's move until I died or succeeded.