Well, I can tell you that SWI 0x12 will decompress LZ77 data. Look it up on GBATEK for the parameters. Then, you need to know the offset that you want you dump your tiles into and then the offset you want to dump your raw into. This is not going to be easy. You will have to find a section of vram (ie, what is shown in the tileviewer) that isn't used during normal play. Then you need to find a section in BG0 (where the raws are. The BG levels don't hold image data, they only say which tiles go where) that is large enough for your raw.
From there, you decompress the images via SWI 0x12 and viola, it shows up.