Zilla having atomic breath doesnt really change this. I mean by no means is his atomic breath strong. I would liken to to the 2014 Godzilla's breath, it drives monsters back, causes some damage, but is by no means a killing shot as some of them are final wars godzilla's in this instance.
Going underground doesn't really matter in this instance as monster X can levitate, and he took the a stronger godzilla attack to the face and got back up. The same shot that instakilled Gigan earlier in the movie.
No I'm afraid I don't see this going in Zilla jr's favor in almost and scenario.