You may try the methods like ultra-filtration or (NH4)2S04 precipitation followed by gel
filtration and ion-exchange chromatography.
Please go through the paper given below and the one added to get more information.
1. Stability of phycocyanin extracted from Spirulina sp.: influence of temperature, pH and preservatives.Chaiklahan, R., Chirasuwan, N., and Bunnag, B. (2012) Process Biochem
If your experimental organisms are cyanobacteria then you can go for classical Bennett and Bogorad method using phosphate buffer and repeated freeze-thaw cycles.
Here lies a protocol using which many researchers succeeded in extracting C-Phycocyanin.