You can downgrade *any* version of PSP using a Pandora Battery and a "Magic Memory Stick". Both can created using another PSP that already have a custom firmware.
There is a hardware approach to convert a regular battery in a Pandora one, it involves opening the battery and desoldering the pin 5 of the EEPROM. However, if you cause a short circuit, the battery could explode.
Other methods to downgrade your 2.81 PSP are upgrading to 3.03 and using an unpatched UMD of GTA:LCS or upgrading to 3.50 and using an UMD of Lumines I.