PSP Updates has a very useful post on how to turn up the brightness of your Sony PSP to level 4, without having it plugged into the mains.

Level 4 brightness on the Sony PSP is normally only available when you are using mains power to preserve battery life, but the following describes the steps you need to take to obtain level 4 brightness at all times.

Brightness Level 4 is bright… but we need the power adapter plugged to keep it. The problem is obvious – we can’t drag the damn power cord everywhere.The problem is over now. We are glad to share a very handy method for keeping your PSP locked on Level 4 Brightness, without any messy process.1, Plug your power cord.
2, Adjust your brightness to Level 4.
3, Start a UMD game/homebrew.
4, When the program launch video is being played (the one with green balls flashed and PSP text in the middle of the screen), make sure you unplug the power cord from the PSP when the launch sound effect is over. You will notice that the brightness didn’t fall down to level 3.And now, your screen brightness is locked at Level 4! You can suspend and resume the PSP, turn it off and back on, or even turn the screen off by pressing and holding the brightness button until the screen is turned off, and none of the actions above will make your PSP lose Level 4 brightness!!! The power saving screen shutting off function will not change the brightness too.The only way to go back to brightness level 3, is to adjust it manually by pressing the brightness button.We should say, this is a very handy way to keep the brightness on-the-go. Level 3 is not enough for some videos sometimes. The only thing you need to make sure is not to touch the brightness button until necessary.Credit goes to Sam for the email hint! =D

The biggest impact of doing this is going to be to your battery life of your PSP, running at level 4 constantly is likely to chew up and spit out your battery in a relatively short time. If you’ve got a film that is just too dark however to watch at brightness level 3, this handy hint may come in useful.