Godzilla: Daikaiju Battle Royale godzilla theme song

The youtube link you posted? It's just Godzilla's Theme by Akira Ifukube. Sounds like the variation from Godzilla and Mothra: The Battle for Earth.

if i remember correctly, GDBR uses mainly remixes and fancreation of classic songs

Sorry gman, its actually Godzilla`s theme from Godzilla vs. King Ghidorah. It plays when he makes his first appearance, right before the first battle scene.

84Goji4Ever,
A part of it that's very similar may have been used. But that scene was void of the first part of the theme and it was slower in the scene you specified.

The track is actually closer to a variation heard in Godzilla and Mothra: The Battle for Earth, but it doesn't quite match the Mt. Fuji scene either. It might just be stock Ifukube as used over the years as well.