Try an UV sterilizer.

This will kill the algae in the water. You will still have to do water changes to get rid of the dead algae, but over the space of a week with a few water changes you should have crystal clear water.

**What won't work:**

Reducing light:

- Algae need light to grow, so reducing the light would seem like a good idea. The problem is that your plants also need light so reducing the light levels enough to kill the algae would also kill your plants.

Reducing nitrates:

- Algae live on nitrates. So reducing your nitrates to 0 or near zero would help. However your plants also need nitrates to grow. And even if you wanted to reduce nitrates, you would have to do regular massive water changes to keep the nitrates low enough to prevent algae growth.

Water changes:

- Water changes will remove some of the algae in the water. But not all of it and there will always be more than enough left to reproduce.