If your on 6.20 your only option is pandora's battery
If you have a Slim with a TA-088 motherboard or higher PSP then you can't use a pandora's battery and our more or less fucked
making a pandora's battery is not all that hard (pull the pin or cut the line) then make a magic memoryStick and done, Note that if the battery was made right you should get a Green lite and black screen on the PSP, If the Magic memoryStick was made wrong the PSP will not come on.
you can even buy Super Cheap pandora batteries here
http://www.dealextreme.com/details.dx/sku.12472~r.24128850