Solution by lavalyn:
The peep must be answered or Black escapes to the strong reinforcements just outside White's walls. After , Black has two eyes.
takes away Black's potential eye and prevents the thrust -
suicide either is forbidden or includes self-capture.
Black dies here.
In case the peep is answered differently, the move order changes... eventually White will play at .
Black is the vital point. White has to play at
to prevent the capture of the marked White stone(s). From there, Black secures the second eye by playing at
. White has the choice of either 'a' or 'b' for the fifth play, but should choose 'a' otherwise White will lose a point of territory. If White tried to close off the potential eye at
by playing there after
, Black can simply play where
is, White can't protect itself from this and will be captured; if White chooses this route then it will lose 3 more points of territory and 2/3 prisoners depending how White chooses to play.