The Dionex AAA-Direct system works well, but what do you expect me to say? The Dionex system costs about the same as any other high-end HPLC system. If you already have a Dionex ion chromatography system, you can upgrade it. Contact your local representative. You need to discuss your requirements in detail to see how well AAA-Direct matches your expectations. It does have some unique features that you can't get anywhere else, and they may be good for you; it has some limitations that may or may not be a problem for you.
If you only have a limited number of samples, you should contract it out. Only if this is to be a routine analysis should you invest the capital and time needed to get good equipment and good results. (Or else it is your PhD research.) Fungi have complex metabolisms. If you think you will be identifying unusual or novel amino acids, this is a job for an expert. Either you hire one, or you work to become one.
There are several alternative methods and systems out there, and I'll let the other vendors speak for themselves.