A few years ago I did consulting work for a new "bio-oil" company working with algae who needed an in-house HPLC method to determine AA's. The method that I developed for them was similar to this one. It worked very well and provided them with the information they needed.
Ann Chim. 2002 Apr;92(4):343-52.
Free and total amino acid composition in blue-green algae.
The technique is straight forward, but you will need a set of 20 amino acid standard before you can start with your unknown sample. HPLC system for detection of amino acid is used by many, but the technique needs some basic modifications with respect to your machine and this can be done when you run a set of standard as a mixture and each amino acid standard separately to be doubly sure of the retention time of each amino acid. Derivitization of amino acids can be done, but getting the derivitization chemicals in India is a difficult without funding.
Once this is done, do an extraction of free amino acids using 100% or 80% ethanol. Since its algae, the extract will contain chlorophyll which can interfere when you are injecting the sample in HPLC. The best option is to lyophilize the ethanol extract or to allow the ethanol to evaporate at room temperature; this will help in slow natural lysis of chlorophyll as well and give u a better extract for amino acids.
Apart from HPLC, I would suggest as a faster method, try paper chromatography (PC) for initial check of the amino acids. I have performed it and it does provide you satisfactory results. You can quantify the amino acids using PC on the basis of size of band and rf just as done for proteins using PAGE.
Many amino acids do not absorb in UV (exepting those which have aromatic nucleus, e.g., typrophan, tyrosine), and being zwitterion they are all not retained on C18 column. For separation on C18 with UV detection you need to derivatize them with a reagent as suggested by Jesse. Alternative chemistries are available and you have a wide choice to carry the analysis as suggested in this JPBA paper.