Pablo Picasso’s genius is only fully revealed when one considers the various facets of his work as they developed through many artistic phases, beginning with his Red
period, continuing through his blue period, and finishing with his period of Cubism.A. period, continuing through his blue period, and finishing with his period of Cubism -> "beginning with" something1, "continuing through" something2 and "finishing with" something3, is perfect and makes sense. But, something1, something2 and something3 must be in parallel. Here, "Red period", "blue period" and "period of Cubism" are not parallel. Incorrect.
B. period, continuing through his blue period, and finishing with his Cubist period -> Here, "Red period", "blue period" and "Cubist period" are parallel. Let's keep it.
C. period, continuing through his blue period, and his Cubist period -> we don't have, "finishing with" in last list item. Incorrect.
D. period phase, his blue period phase, and his phase of cubism -> It seems beginning is connecting all different periods, which doesn't make sense.
E. period, his blue period, and his period of cubism -> Same as D.
So, I think B.