There are six parts to the boss:
A. Main body
B. Main gun
C. Top right
D. Bottom right
E. Top Left
F. Bottom Left
The most important thing about this boss is that they exist on different areas in the 3D space, i.e. they are stacked. C, E are on the top layer; A,B are on the middle layer; D, F are on the bottom layer. As the boss flips around some targets will become unavailable to attack. Another complicating factor is the very short time limit you have to destroy the boss. Because of the short time limit, a hypersword is almost required, but it is possible to get by without none. However, depending on how fast you defeat it, afterwards two or four extra enemy formations will appear, two of them being red enemies for continuing the maximum chain on stage 3A.
Before the first firing of the main cannon, there is a small gap between the main cannon and the top left segment. To start with, you need to wedge your ship in that space.
From there you have some choices. Typically, strategies are set apart by using 1 or 2 hyperswords, depending on how safe you want to play it against how many hit & grind points you want to squeeze out as well as contributing to weapon bonus timers.
1-hypersword, super safe way (less points):
http://www.youtube.com/watch?v=Ko2hr1Yr8EY&t=1m11s
1-hypersword, less safe way:
http://www.youtube.com/watch?v=9msKYqaAdB4&t=1m41s
2-hypersword, less safe way:
http://www.youtube.com/watch?v=yNQNUMLqjSc&t=32s