Unlocked by taking the Flying Saucer through to the ending of the game.
This is most easily done with the Flying Saucer from 7-8, which is the last opportunity to acquire one.
This is extraordinarily difficult to do, as the Flying Saucer dies in one hit, and requires you to make your way through two bosses and ten other zones.
Note that the flying saucer, unlike all the other ships in the game, treats the game as a wrap-around - you can fly off the top and appear on the bottom of the screen, or fly off the front and appear in the back.