I think it is hart to understand i did it also wrong for a long time. The black pieces of the boss is armor and you can only damage him if you shoot at the 4 red balls or the eye. Maybe Wolly is making that to better in the steam version I hope.
eh, pretty easy to see that when you shoot the black nothing happens, and when you shoot the bosses red weak points there is slight screen shake and a visual notifier that you dealt damage in the form of the boss flashing.