So you have a GCN that was made into a portable system?

Well for starters you have to ask yourself how many hours do you plan to play portable. Then you would look for battery setup, and the materials and setup to convert to the correct power.

Otherwise you will need to literally search for adapters that matches the juice the GCN requires. I would imagine you hooking up a tablet/phone battery to a cut off GCN plug in some sort of method. But beyond figuring out which is positive or negatively, it would also require you tearing down a GCN PSU, as well. The end result would probably be a raid of AA batteries, or some other off-brand electronic battery that is available through orders like the GBA battery.

Without the right tools it would be trail and error. If people can do the same thing for a Electric-motorcycle or even a phone I am sure you can do it as well.