I don't really know what hard soda is supposed to be... still sweet yet infused with moderate alcohol? So you could just mix like a rum and coke. Or do gimmicky brews that aren't really a natural process of getting from A to B. Or you could do a straightforward brew that is prematurely snuffed by keeving, which starves the yeast of nutrients before sugar is near gone. I don't think that is an easy process though.
I think that is what they do in Normandy to make sweet cider, which tastes nothing like conventional cider but more like the most sublime apple soda. If you buy some that has had a few thousand mile ride in a ship, the taste is crap... probably because not enough alcohol to preserve the delicate taste. But in France it gives the best tasting drink I have ever had or probably will have. Maybe they don't make much fancy sweet cider there anymore... I think it never was as popular as dry.