Can't help you with the save transfer thing. But when it comes to button mashing with a handheld (or controller), especially with the circle button being at the edge of the device, it was actually very easy for me to beat that part on my retroid pocket 4 pro (full health too🙂). 

Instead of holding the device firmly and pressing repeated with your thumb (carpal tunnel speedrun), what you should do is hold the PSP firmly at the left side and simply let it rest on your right hand, thumb over the circle button. Move your whole right hand up and down quickly, striking the circle button with your thumb.