Found under the Challenges option the main menu, this way of earning Fight Money is surprisingly rather overlooked. This is an incredibly easy way to get a one-time drop of Fight Money, as these demonstrations play as videos and nothing more. You don't have to play you just have to hit Light Kick (A/X) to progress between each slide of new information.
Demonstrations are split into four sections Beginner, Intermediate, Advanced and Character Specific. Completing every header under the Beginner, Intermediate and Advanced headings will net you 1000 Fight Money each for a total of 3000.
The Character Specific heading is even more kind, offering 1500 Fight Money plus some Character Experience Points for each heading viewed. These are actually incredibly useful in general, too, and are well worth paying attention to rather than simply leafing through them each page of this contains vital information on how each character works. All of these Fight Money bonuses are a one-time deal.