Purchase the costumes from the Store in the main menu. The total cost of all the costumes is 13,000.
I completed the Story mode before buying any alt costumes and had enough to buy all at once, plus a couple of characters.
If you fall short, however there is an easy solution:
The quickest way to grind points was to set up a custom match in Battle mode with a dummy controller. Set lives to 99.
I chose Vilgax as my primary controller (tried a couple of other but their throws weren't as effective) and any character as the dummy controller.
For the level, select the first Powerpuff Girls stage. The giant robot in the background will knock away the side buildings after around 45 seconds, leaving a very small platform remaining.
Start grabbing the dummy and throwing it off the side of the platform for 40 points per kill. Picking up the Synergy items net you around 1 point.
Try not to fall off the edge, as you lose 20 points per death.
Using this method, it took approximately ten minutes for 99 throws and I obtained 4k+ points. The most I received was around 4,500 points.