Ahh, this game brings back memories!
PSicture can grab
Brigandine's textures, character portraits (small, but beautiful!), battlefield tiles, backdrops, even spell effects... just about everything aside from the sprite sheets you're most interested in it seems.
For the sprites, I'd recommend checking out Barubary's awesome 2D Swiss army knife,
TiledGGD.
Here's a sample setup on a 2048 byte-per-sector game image showing where the sprites are (look at the settings on the right-hand side). I think all of them might just be sitting out in the open! You can see the image data at that offset, but darn it if the game didn't hide the sprite palettes pretty well. They're not obviously occurring either before or after the sprite sheets.
I'll bet the reason why the sprites don't show up in PSicture and other TIM viewers is that the developers removed the palettes that would occur in a standard TIM header, and shoved them all into one shared place somewhere. That way they didn't have to store a new sprite sheet every time they just wanted to palette-swap a player or enemy sprite (and I recall
Brigandine does quite a bit of palette swapping). Just my theory. The best way to proceed might be to use a VRAM viewer (I recommend
creaotcheann's PVV) to grab the palettes from a savestate made during battle. TiledGGD supports grabbing the image palette from a separate file.