I got a PSP with FW version 3.30 OE-A which is very old
Trying to start 6.60 or 6.61 update, it was giving an error “cannot start game” – which is as expected for old FW as I found out.
Tried all kinds of other solutions, like Hellcats recovery flasher standalone with zero success – running the eboot was just going black and then shutting down the PSP.
This page solved the issue, strangely enough it uses Hellcats recovery flasher as well but it just works https://www.psdevwiki.com/psp/Updating_From_Old_Custom_Firmware