If the plane you are going to be taking offers access for a portable power supply, you can get an adaptor for a variety of electronic devices (the PSP should be fine) that will let you plug the AC power cord into it at stores like Circuit City.
If you're going to go with battery power, then I definitely reccomend getting the newer Sony battery with 20% more battery life. I've been using one for months, and it's definitely a noticeable improvement over the older batteries. Getting the most out of your PSP battery life has to do with brightness setting (I usually use medium), volume (earphones will make it last longer), and the game you're playing. When I moved to Japan last year (12-14 hour flight), I had two older PSP batteries that worked out fine; I used up the first battery, but had plenty of juice left in the second by the time the flight landed.