Battery powered RGB matrix board
I would suggest picking up a decent lithium battery meant for RC applications. They're cheap, and readily available. Chargers are also fairly easy to get too. If you decide to invest in something decent you can keep using it for future projects. 

It's fairly straightforward to calculate how long the battery will last. It'll depend on what voltage battery you get though. Say you get a 3s LiPo battery with 1Ah of capacity, it has a nominal voltage of 11.1V. At full load of 4A draw the converter will draw just under 2A from the battery. A 2A draw from a 1Ah battery gives you 0.5 hours of run time.

You'll need to add in overhead for the efficiency of the converter, and also to avoid discharging the battery too deeply. Ideally you want to keep the battery above 20%.

Digikey and other suppliers have plenty of compact easy to use DC DC converter modules which can power the LED controller from the battery.

Standalone DC DC Converters

Board Mountable DC DC Converters

Don't forget these converters are pretty efficient, but they're not magical. Make sure there's adequate cooling available or you might burn your head. All of that is specified in the data sheet, so you can get an idea of what to expect.