Mycosporine-like amino acids are generally synthesized in response to UV radiation intensities among many other influences and the best organisms to extract MAAs from are the planktonic photoauthotrophs since they require sunlight to photosynthesize and are the ones most likely to get exposed to the ultraviolet radiation. The best candidates for such large scale extraction shall be diatoms and unicellular green algae like Chlorella, and cyanobacteria etc.
Jeffrey et al. surveyed MAAs in a large number of microalgal isolates:
Jeffrey SW, MacTavish HS, Dunlap WC, Vesk M, Groenewoud K (1999) Occurence of UVA- and UVB-absorbing compounds in 152 species (206 strains) of marine microalgae. Mar Ecol-Prog Ser 189:35-51
As Dr Mukjerjee notes, growing the cultures under high light will promote up-regulation. In my experience, irradiance (visible, not necessarily UV-augmented) high enough to achieve light-saturated growth causes a significant increase in the cell quota.