I looked and the music that plays in the battle with Lima is "Battle8"
Just saw you already found it. Yeah rpg maker has some real banger songs^^
I also looked for potential bugs with the world fragment but could not find anything yet. The jaguar quest returns your lost fragment to you like intended. And the Ice Dungeon also seems to work as far as I have seen it.
Did you still having this problem? I alsoways could take a look at your savefile to figure out the potential bug.