"What do I do...?" if you don't say this multiple times, you haven't actually played the game.
Why? Well, the game consists of essentially two parts. Part I, you walk around a city and try to find the boss. This part is slow, annoying, but playable. However the second part consists of fighting said boss. This is where all hope is lost.
Boss battles are poorly explained (even in the manual) as to how to win. It's extremely easy to be curbstomped by a boss, while Godzilla does little more than wander back and forth. When you do manage to damage an enemy it feels like luck, and I will admit. Of all games I've played beating a boss in this one feels the most rewarding.
The combat seems to be an odd mix of button presses, card games, and luck. Without really committing to any of the above.
The end boss 'Bagan' is possibly the most fascinating aspect of the entire game. While you can find powerups in various levels to become "Super Godzilla" and curbstomp him. The actual fun part is that TOHO and ATARI have disowned him. To the extent the fastest way to get banned on the Atari Forums. Is to mention him.
If you're a diehard Godzilla fan, such as I am. The game is a great addition to your collection, however of the Godzilla games out there. Don't expect it to be "Super Fun".