Remove your mind from the gutter... The "Fantasy" in Fantasy Zone refers to the cartoonish atmosphere (not a boob-ish atmosphere).
Fantasy Zone is a fairly unique horz cute-'em-up with good game play and a couple of ideas to make it different than other games.
Your ship is controlled by a joystick and two buttons (shoot & bomb). The screen scrolls horizontally both ways, so you can fly either direction - in fact, the screens eventually wrap around and is a finite strip - if you keep flying right, eventually you wrap back to the first screen from the left (and vice versa). This is important because you have a very specific goal to end each round/level. You have to destroy all the "main" boss-like motherships that are crapping out minions like there's no tomorrow. You can kill or avoid all the myriad of minions, but the round will not end until you have killed all the motherships.
To aid you in your quest, there is a radar-type display at the bottom middle of the screen that shows where the motherships are so you can head after them. The radar shows equidistant blocks - if it is greyed-out, the ship is destroyed, but if it is red, the ship is still there. The longer the stage goes on, the more minions are belched forward.
So, when you kill the last mothership the round is over - Oops...except then, the main boss comes out for the final battle for that stage. The problem with the main boss is that if you die when you are fighting him and still have ships left, then when you continue, the boss is new/whole again, you don't get to have the benefit of the damage you inflicted before croakage.
The other main factor in the game is the money/upgrade purchases. During the round, gold coins fly around. You gather them to collect money for upgrades (separate from points). Then, when you see a balloon floating around that says "shop" (usually at the start of new stages), you fly into it and get to buy all kinds of crazy crap.
Of course not of this would matter if the action wasn't good. The constant shifting left and right and the good A.I. of the enemies make FZ a very compelling game that treads that fine line where it is very challenging and yet very satisfying to control and play. The cartoon graphics can be fun, though they can also look like someone ate a bunch of pastels and puked them all over the screen (in a good way).
Lots of good-time to be wasted here...