Replay. Ignore the rest; I was messing around. Stage 4's "waterfall" can be, fortunately, tackled somewhat easily if you start off a bit to the right when the first big fairy enters. Move left, streaming the large bullets. You'll note that I jump through a gap in the waterfall. After a fair amount of testing, this is probably the easiest way through it, as going "up and around" that extra little segment will most likely get you walled when the other fairies enter from the other side.
The Stage 6 scenario is, unfortunately, impossible to bypass without taking a hit AFAIK. The leftover bullets are the largest problem as they severely restrict your movement, effectively pinning you which leads to getting nailed by the ring of fairies (aimed at you by the way) or the aimed bullets from the next wave.