This was probably the biggest wall I had to overcome when I was trying to learn Mars Matrix. This video is of the strategy I eventually came up with. Recorded from a savestate in MAME (But the boss is exactly the same in the DC version, from what I can tell). If the boss is still alive by the next bullet pattern, you can just kill via sucking up bullets until near the end of your meter and releasing them on the boss (This is why it's important to only do that once on the last pattern of this video)

Hopefully someone finds it useful.