I think the simplest way will be analysis by a solid sampler module connected to a TOC analyzer. Before that we have to ensure that the sample of algae should be powdered and moisture free. Though we have the equipment, never tried such a thing. We are analyzing mainly the sediment samples.
I would recommend to determine the C/N ratio (in solid samples after drying at 60oC for three days or at 105oC over night) by means of GC/MS. Only a few mg is needed, so you need to homogenise your sample carefully before collecting the final mg- amounts.