A reliable acquaintance who is working on a doctorate concerning algae told me the other day that there are roughly 300,000 species of algae!!
She also confirmed that chlorine, in the proper dosage, will kill every one of them.
What I take away from that is, while we probably experience hundreds of species, we should not feel our particular pool is unique.
Chlorine gets it all and you are not growing some super-unique type in your pool making it impossible to kill. Chlorine is the answer. The proper dosage of chlorine (and maintaining it at that level) is often what gets neglected.
Food for thought.