The shiny shape shooter you refer to is not the boss of the level, just a standard enemy. Kill him if he's too much of a distraction, but I just wait for him to clear some blocks so I can get through and then ignore him the rest of the level.
When you get to the actual boss, hit him 3 times to kill him. The fake ones look like they're made out of sticks and burlap, the real one has big white eyes. Avoid the fireballs and you will prevail.
I have beaten the game before, and I found every secret along the way (after you complete the special world, the main map colors flip! kinda weird). I'm still trying to get an SNES emulator working in Linux, for the sole purpose of playing this game once again!