I tried the search and Google with no avail, and apparently there is no official soundtrack. So, anyone has the rips from the game?
Thanks in advance!

I've also been looking for this. I hope someone can find a rip!

Well. There is an official soundtrack, Danball Senki LBX Battle Soundtrack, it's not complete though. There was a gamerip for PSP version (Boost) floating around once, but I think it's gone.