To start off on a randomly interesting tidbit, this movie had somewhat of an identity crisis in the US, as it was also titled as "Godzilla vs. The Bionic Monster" and "Godzilla vs. The Cosmic Monster". What's wrong with "Godzilla vs. Mechagodzilla"?! Oh well, we start this off as someone gets a [strangely accurate] fortune from something or other that says something like "If one sees a black mountain in the clouds, a monster will try to destroy the world... and two will rise to save the world" or something like that. I don't know if that's it exactly, but that's what happens... not that it matters since I usually only describe monster scenes most of the time, even when I say I'm not going to. So, on that note, our harbinger of death is none other than... GODZILLA?! ... Uh-huh... because surely you'd fall for that despite the title, right? So, shortly after "Godzilla" starts wreaking havoc, Anguirus comes along and battles him, only to leave with a broken jaw... but not before destroying some of Godzilla's "skin", revealing that he's really made of a material known as... Space Titanium... right... I guess the writers were feeling particularly lazy that day. Eventually, this fake Godzilla makes its way over to a populated city... only to encounter the REAL Godzilla! The fake Godzilla then gets rid of its disguise, revealing itself to be none other than Mechagodzilla, made by a race of aliens... yes, there's MORE aliens.
This time they're Gorilla-Men things! ... So yeah, Mechagodzilla was made so they could conquer the world (OFCOURSE!) or destroy it, if the prophecy is anything to go by. But anyway, Godzilla and Mechagodzilla do battle, which eventually ends in a tie (due to both of them being severely injured). But after much exposition (and quasi-ripoffs of James Bond sequences) the 2nd savior of the Earth is awakened: King Caesar, the lion/dog/god thing! So ya, King Caesar fights Mecha-G, gets his booty handed to him, Godzilla comes along and teams up with him (though Godzilla ends up doing most of the work anyway), and Mechagodzilla is defeated... until the sequel.
I got very lazy on the plot description, but I thought that this was one of the better Showa movies... especially seeing as this one had [basically] no stock footage.