I'll have to agree with the acid suggestion. Hydrochloric acid works the best (just wear rubber gloves, goggles, and a respirator). It's often sold as "muriatic" acid. You can pick it up at just about any pool supply store or sometimes Lowes/Home Depot.
You'll also need a stiff push broom to scrub with. You may want to dilute the acid down with water (25 HCl/75 H2O) to start and then work your way up on the tough stains. If you get a really tough stain, pour the acid on straight and step back a little (cool green theatrical effect).
When you are done, hose it off (just don't let it run off onto your yard, unless you like yellow grass).
I used to use HCl to clean concrete pools years ago. Works like a charm and leaves them nice and white. There's also no etching if you dilute the acid properly and rinse shortly after scrubbing.