It's not hard, but it's not quick either.
Open the rom whose palettes you want to edit in SNESPal:

Jump to the offset where the palettes are located:

For battle characters, there are 16 colors. You have to manually change the colors in your graphics editing program (I use Tile Layer, but should work the same using Tile Molester). SNESPal displays colors as values of 0-31 instead of 0-255, so multiply SNESPal's value by 8 if you want the colors to match exactly. The quicker and less accurate way would be to just match the slider positions for the R/G/B values:

When you have done this for all 15 colors (the first color is background, make it whatever works for you. I chose white.), your palette will match the game's:

Each battle character has a different palette, so you'll have to repeat the process if you want to see the next character's (Kain) palette, and so on.
Incidentally, if you want to actually
change the game's palettes, SNESPal will allow you to do that as well.