Yeah Japanese tables are tedious compared to Roman language efforts.
Many approaches, none quite so nice as simple relative search (though relative search in some forms can come back) as Japanese does not have a fixed order alphabet.
Most will try
1) Finding the font. The vast majority of the time the order in the font will be the same as the encoding for the game.
2) Finding the text. If you know where the text is you can change it and run the game (be careful using savestates as games might load things into RAM well ahead of when it appears on screen). Change a whole line to all one character and if you find a section with just that one character note where it is and then start trying other things there. Very tedious but will get it done.
3) Hoping it the same order or even encoding as known ones. Japanese coders are just as lazy as coders anywhere so they will often copy at least segments of Japanese language encodings. ShiftJIS and Euc-JP being among the more notable here, though good old unicode is also a thing
http://rikai.com/library/kanjitables/kanji_codes.unicode.shtml http://rikai.com/library/kanjitables/kanji_codes.euc.shtml http://rikai.com/library/kanjitables/kanji_codes.sjis.shtml
4) Some fonts will include an encoding value with them and not just be a pretty picture. On the DS then the popular font format NFTR is this, not sure what we have on the PSP.
5) Check for mathematical and linguistical relationships. I mentioned shiftJIS and the like above but the language also has things that those might use to learn them (various tests and dictionaries) so copying that is a thing. Mathematically is both code based (some games will order the font in terms of most popular, first to appear in the script and so on) and language based (for English then every word has a vowel or a y, space is pretty common and similarly most words are not long, general letter distribution is... see scrabble, and so on) will see you wanting to know some Japanese but if you have it then great. Japanese knowledge can also help if it decides to include the ?kuten after their respective characters in the kana section rather than after the section containing the base kana as seeing that can help you figure that out more quickly.
6) You follow along the game's code as it decodes the script, fetches the relevant character and note it all down, or possibly even find its decoder if it is not a massive long bit of code.
There are some other things some do, and plenty more specifics but that is the main approach most would take.