OK, I beat that boss today. I had my weapons upgraded fully, bought the best shield (did not equip it at this time), equipped the beam saber and made sure I had a Shot Gun in storage as well as being maxed on Medium repair kits. My body was one less than maxed on all levels.
Head towards the boss killing everything with a mix of beam sword and shot gun. Meter you shotgun usage so that you run out of shotgun about half way through the boss's base. Then you can have room to grab the Powered Bazooka that sits in...the Bazooka Room. Don't fire it yet.
When you finally get to to boss, equip the shield and hold down the fire button in his face so that he gets beam sabered at maximum speed. Ignore the random fire from the ceiling and such. This is kind of a "Mother Brain" fight. Your health will drop very quickly during this so make sure you are healing if you get below 1/2 health. You will need every Medium repair pack you could carry. Eventually his mid section will open up, instantly switch to the Powered Bazooka and hold down the fire button until he dies. If he doesn't die before he closes up, you'll probably not survive another cycle. I'm sure its possible to use more skill that this. You might be able to Lock yourself to the right and dodge the big glowing ball (which is the vast majority of damage to you) but I got sick of dying that way and just bought enough kit to pass it this way.
After this you get a jump pack that lets you double jump. You can then cross the mountains to the south, see a cinema, and explore a new map. Also, the new shops will be able to upgrade your Gear to higher levels than the previous shops. I hadn't maxed my body or legs yet, but I'm glad there is more room to grow.
This game is good, btw.
