Classic Battle is reminiscent of arcade fighting games where you simply fight through a series of characters and at the end, there's even separate arcade style endings for every character.
From the main menu select Single Player -> Battles and select Classic. Select a character and choose 'Very Easy' difficulty to make it fast and easy. There are 10 opponents which won't offer much resistance on the easiest difficulty. If you ever lose a match, you can hit retry and resume where you left off.
Check which characters you've already completed this on by going to the Archives and viewing the Characters section. Characters you've completed this on will have their classic battle ending unlocked and viewable here.
You will also unlock "Rise to the Top" after completing Classic Battle for the first time.