Man. Nuking this post. Had Symphony of the Night confused with one of the GBA ones

tl;dr, may just write a program that can create a palette from all the images you have at least, because I'm having trouble finding one that could do that for >256 colors. (Imagemagick may help you if total colors are <1024.)

But extracting palettes from a game is not something you can do very automatically, unless someone has already done the reverse engineering work. Depending on the hardware some emulators might display the palettes to display the current scene (because the hardware would need that info to display it) but that doesn't reflect how the game stores the palette, or where, or how many colors.

Edit:
I kinda wonder how much of it is here:

This is what is seen in NO$PSX in the first gameplay section, but it's probably not all of it, and parts of it are animated. I would probably not expect to get all of it, even this is quite a lot of colors. 1822 unique.

Edit2: The above image is scaled wrong. So... here's this:

But it's over 2,000 unique colors now and that's probably not all throughout the game. So it's gonna end up as far too many to be useful I think. There are also colors in the scene that aren't in that set, so who knows.