That definitely helps. It looks like you want to change it so that, for example, the graphics are shown with palette #1 instead of palette #3. I looked into the game and those graphics are drawn as sprites. In order to change which palette they use, you'll want to modify OAM (object attribute memory) data. If you're unfamiliar with OAM, you should probably read up on it. The NESDev OAM article
looks pretty decent. It's the data that defines the tiles and locations of each sprite.
The OAM format is four bytes per sprite: YY TT AA XX, where YY = sprite y position, XX = sprite X position, TT = tile number, and AA = attribute data. It's AA that you're concerned about because this byte specifies which palette the sprite uses.
If you pause and use a memory viewer, you'll see that OAM is written in RAM at $200. The nice thing about this situation is that the sprites stay in one place (in most games, each sprite moves to a different memory location each frame). If you go ahead and start changing sprite memory, you'll notice that every time you change a byte, one 8x16 tile on the screen flickers for a single frame. (On the next frame, the game re-writes the sprite data and fixes what you've changed.) This lets you easily figure out which memory is for which sprites. I kept messing with them until I found the sprites for the characters on the screen.
Once you've found the memory for the sprite you want to modify, you can search the ROM for that data, and then change it. For example, the sprite I wanted to change had the data: 28 20 03 28 28 22 03 30 28 24 03 38 28 26 03 40 38 28 01 28 38 2A 01 30 38 2C 01 38 38 2E 01 40 (eight 8x16 sprites gives you your 32x32 graphic).
When the data is stored in the ROM, the x and y values are usually stored as relative values, which means it will be different in the ROM than it is in RAM. If you search the ROM for "28 20 03 28 28 22 03 30" you wont find anything. You can do a wildcard search and omit the x and y values: "28
20 03 28 28
22 03 30
" becomes "? 20 03 ? ? 22 03 ?". That search lead me straight to the sprite data I was searching for. Once you find it, you can change the attribute byte of each four-byte entry to use a different palette.