Catalyzes the four-electron reduction of biliverdin IX-alpha (2-electron reduction at both the A and D rings); the reaction proceeds via an isolatable 2-electron intermediate, 181,182-dihydrobiliverdin. (2R,3Z)-phycocyanobilin + 4 oxidized [2Fe-2S]-[ferredoxin] = biliverdin IXalpha + 4 H(+) + 4 reduced [2Fe-2S]-[ferredoxin] Belongs to the HY2 family.