I would argue that the major achievements of the United States during the 1920s had to do with improving the quality of life enjoyed by the American people.
The main feature of the 1920s in the US was the increasing wealth that many people had and the increasingly high standard of living that they could purchase with that wealth. It was during this decade, for example, that Henry Ford's Model T became widely affordable. The fact that many American families were now able to own cars increased their standard of living. In addition, the creation of things like movies and of various household appliances made life easier and more fun for the American people.
For these reasons, I would argue that the major achievement of the '20s was a higher standard of living for the average American.