Well, one way of combating algae is to put in fast growing plants, they'll suck up the nutrients that the algae would normally use. Try buying a small bunch of hornsworth or whatever it is and leave it at the top of the tank, floating around.
A) it'll block some light from the sand, so less light for the algae to use
B) create a nice shadow for the betta to feel secure
C) suck out some CO2 that the algae is using up also.
Just trim it if it gets too invasive, and throw it out or put it in another tank.