There are five bonus stages in the game. Here is how to access each one:
Stage 2 - When you see a hole in the wall at the bottom of the screen, fly down there.
Stage 3 - When you reach the lower level of the stage, there is a platform in the ceiling that drops down. When it drops down, fly just below the part where the platform was.
Prerequisite: Destroy all of the ground targets in the stage up to that point.
Stage 4 - In the last set of Moai heads (they look like Easter Island heads), there is one laying down which will lift itself up. Fly behind it.
Prerequisite: Nothing must be highlighted on your powerup bar.
Stage 5 - Fly just below the ceiling before the narrow corridor.
Prerequisite: The hundreds digit of your score reads 5, 7, or 3.
Stage 7 - Just after the long downward slope in the second half of the level, stay close to the ground and fly into the wall formation shaped like this:
(key: dots are empty space, lines are walls, the asterisk is there your ship should be.).
When you clear a bonus stage, you will end up in the next level. That's right, you don't have to fight the boss of the level you were in previously. However, if you get killed in the bonus stage, you will be taken back to the regular level, and will not be able to reenter the bonus stage.