This boss keeps splitting in two when hit, but you'll notice the two new units are smaller than the original. This splitting process does not really harm the boss, only when at the smallest single unit level your shots will cause damage. The strategy should be to attempt to minimize the number of enemies on screen, we should concentrate on splitting the smallest group on screen until it reaches the base level we can actually damage, and destroy these before continuing splitting the boss further. If we do it right there should never be more than four enemies on screen.
To avoid accidental splitting the standard weapon is the best suited for the job :)