So first we need to confirm its Bluegreen Algae (Cyanobacteria). If you remove some from the tank, is it more like slime or more like a mass of threads? If it's like slime, 99% chance its Cyano. If its not Cyano and an actual algae, then we need to look at light/co2/plant mass/nutrient balance.
Now, BGA doesn't respond to the typical methods of algae removal, because it's a bacteria (but a photosynthetic bacteria...so it's almost like a weird plant/bacteria hybrid type of creature). And since it's a bacteria, it requires some more drastic measures to eliminate.
The main two options are:
A) Tank blackout.
Remove ALL of the BGA that's visible. Clean your tank as much as possible, clean your filter well, and water change. Then turn off your light, and wrap the tank in black plastic so that absolutely no light can get in. Leave it this way for 3-5 days. With this method, some people report success, but sometimes the BGA comes back and requires additional attempts.
B) Erythromycin treatment.
This is an antibiotic, and it kills the cyanobacteria cyberpunk. It shouldn't harm your biofilter, but it MIGHT, so make sure to check your ammonia/nitrites during/after the treatment. Also sterilize anything like nets, best mask
, buckets, water-change hoses, etc, because you could reintroduce the bacteria into your tank after the treatment (this also applies to the blackout method)