What you NEED to do is kill the algae first, then vacuum it out. That means lots of bleach. 1 gallon of 8.25% to keep your chlorine level at 15ppm may well do it. Each gallon of 8.25% will add about 15 or 16ppm of free chlorine to your pool.
Once you do that, you want to vacuum it out. I used to use a 1.25" vacuum hose with a 3/4" PVC double female connector in the hose as an adapter to the Intex drain, but you'll have to wash the filter medium a lot to get all the algae. Alternative, you can get a Pool Blaster (expensive-$300) but they are rechargeable and last for years, and won't use any water. Get the smallest.
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