Middle daughter bought used trailer that had been sitting for several years and had the problem you have. She filled and emptied several times, then bleached it and let sit overnight, drained, filled, drained, filled, bleached, let sit over night, drained, filled, drained, filled.. bleached again, let sit several hours, drained, filled, drained, filled. She also cleaned the filter on the water pump a number of times. They carried drinking water in 5 gallon water jug then. I don't know if they got the algae completely out or not.
When we bought our used trailer, it only took a couple of treatments to get rid of it, only had to clean pump filter a few times. No problems since.