It is possible but it would have to be on a game by game basis. I can't see an option for a plugin to universally increase render speed or play speed being an option here, mainly as it is only an option on some other devices in very specific conditions and usually come with a list of serious asterisks 30 pages long.
Same ideas as on the GBA, DS and whatever else we normally see that question asked for around here.
1) You hack the game to speed up the text. Various approaches here ranging from seeing if you can abuse any in game options (fastest may not be the fastest the game allows, if it will allow you to skip if replaying a section then see if you can flip the bit in memory that says this is a repeat) to actual hacks.
2) You hack the game to speed up the animations, or maybe skip them entirely.
3) If there is some kind of internal render counter you might mess with that, however that can be tricky and lead to all sorts of fallout.
4) Any cheats that speed things up you can also add here -- some games might assign running to an item, while you said you are power levelling that means probably don't want to skip battles but if you want to skip weak battles then that is a thing. Whether you go fully into cheating here is up to you.
Some things can be reasonably entry level hacking but most of that is on the more advanced side. You will also be messing more with 3d animations, which in some ways can be easier and in others harder. Battle animations and walking animations (a lot of animations will be things like for 3 frames do this and move this far, repeat until 30 pixels have been moved and then stop, change this to 6 pixels and you get something like double the speed, change it to 30 and it might be essentially instant. Can have some odd effects in some games with regards to things like random battles and phasing through doors or animation triggers but they tend to be found out soon enough).
This is all quite annoying to do on systems we have nice debuggers and emulators for, for the PS3 this gets even more fun. Far from impossible but there is a reason you tend not to see such things done.