So no one else wanted to play Single Player VS mode. That must be why no one else ever noticed this.
So basically what you have to do to get these credits is finish the game on VS Mode.
The credits don't actually use the Godzilla theme in the background, I just had the Godzilla Theme playing in the background(which is by Akira Ifukube)
This also proves that Mechagodzilla 2 is indeed in game and was never supposed to be playable, instead he was meant to tease the next movie, Godzilla vs Mechagodzilla 2.