Thanks go to sometimes hacker, C.K. Sample, III, author of PSP Hacks for contributing this how-to.
So you’ve heard about this homebrew thing that all the cool kids have been doing, but you have already upgraded to version 2.6 of the firmware so that you could play all the latest and greatest games on the PSP. Fortunately for you, some very diligent hackers have been working round the clock to discover ways to get around the limitations put in place by the latest firmware.
The solution isn’t in the form of a downgrader, but rather in the form of an eLoader (EBOOT loader) that lets you use Grand Theft Auto: Liberty City Stories to run homebrew on a PSP with version 2.0, 2.01, 2.5, and 2.6 of the firmware. Not all homebrew will run via this method, but there is a rather easy to read compatibility chart and I’m sure more things will begin working in future releases of the eLoader.
To help you along in your quest to homebrew, here’s a step by step (with pictures!) guide to using the eLoader: