The game was mentioned for the first (and last) time in the May 1995 issue of Nintendo Power. However, the issue said that the release date was April 1995, but it was already May of that year. The game was not mentioned again in any magazine and no copies of it ever existed.
Nintendo Power was able to review the game in Nintendo Power issue 72, although it was never released. An explanation could be that the Nintendo Power writers had gotten copies of it, but Toho or Nintendo decided to not release it.
The game would have probably just been a translated version of Godzilla: Monster War, with all the same monsters and stages. The Nintendo Power teaser describes the game as a tournament fighter where the player had to experiment and master their monsters' moves to become successful.
Confirmed monsters for the game include: