I lack the game here to pull apart and have a look at but in general
You have two primary approaches.
1) Emulator and hardware based approaches. PPSSPP is pretty good actually, in older consoles you might have seen people disable certain layers) and I am not sure what the custom firmwares are like for in hardware screenshots these days but that is the path people head down.
You need not play the game properly either and can cheat all the way to them, or perhaps even mod the game to display them, more on that in the next point.
2) You do the ROM hacking bit. The tool most use to pull apart PSP games is called umdgen. From here you get to learn ROM hacking if you want to be guaranteed to get them but there are things you can try with more limited skills, especially on the PSP where common formats or formats commonly seen in games are easy enough to come by compared to the DS or something.
So yeah go through the game looking at directory names (you can eliminate things as well -- if a directory says sound then it is probably not pictures) and file extensions. If it is a nice PNG or something then great, if it is something more custom then you can learn to figure out how the formats work (the PSP is a nice split between high level stuff and low level stuff that is designed to go right into the graphics hardware like most older consoles).
Going back to 1) then if you have a nice directory with with however many files for however many events then you can just extract and insert over; if event 1 is quick to get to in the game (either from the start or from a save) then extract say the rare boss event or whatever and overwrite event 1's image, the game will hopefully then dutifully load what it thinks is event 1 but contains the rare event and you can do screengrabs and whatever else, and all this without necessarily knowing the first thing about the format of the images. In cryptography this would be akin to something called an oracle abuse attack where you have a black box you have no idea of the mechanisms for but can feed it whatever you like and have it decode it.