The essence of the game is that you run around smashing cities and battling the military (who are controlled by the other players), and get mutations along the way, until finally the surviving monsters gather and beat the crap out of each other in a giant monster brawl in the wreckage of a ruined America!
Haw! Take that, RISK! If only more board games ended in monster skirmishes, it would make for much more interesting play experiences. An old stand-by like Clue would take on a completely fascinating milieu with such an addition- not only would you have figure out the identity of the murderer, but then take them down after they transform into a colossal perversion of science upon being discovered.
But I digress.
Some more pics from Giant Monsters Menace
Here are the game pieces for the monsters and military forces (I call orange!). The two beige pieces in the monster picture (named “Mecha-Monster” and “Captain Colossal” respectively) are apparently special giant military units that can be used in conjunction with your tanks and planes:
And some examples of the mutation cards that impart special abilities to your creature during the course of play:
Further details are available from the Avalon Hill website (including an interactive demo).