The point is, the core is its right hand. You actually have to destroy it to win. But, to do so, you have to destroy the left hand (2000 hp, unaffected by techs) or the body (10000 hp). And the other hand will drop its defense and revive one of these in a few turns and then become invincible again until you destroy another part.
And the body loves using really strong magics to keep you entertained meanwhile. And Frog has a really pityful defense so :(
Personally, I think I'd freak if I ever really saw an alien. What's strange is that there are multiple sightings of UFOs and/or extraterrestrial objects in America, but I don't really hear anything anywhere else.