It seems that many games does require the 6.xx firmware now and especially one particular one which everyone is dying to play. Monster Hunter 3.
In any case, there is a Prometeus 4 Firmware (not released by original author), but nevertheless allows players to at least play some games from 6.xx firmware.
Again, simply download the file and then put it into the root of your PSP (with directory intact). Run the Updater from XMB and there you are. Do remember to reboot it when asked to press [X]!