The correct answer is establishing the direct election of U.S. senators.
The statement that describes an achievement of the Progressive movement in the early twentieth century is "establishing the direct election of U.S. senators."
When we are talking about the progressive movement we are referring to the active social participation of a group of Americans from 1890 to1920, that wanted to change some problems that the industrialization and government corruption brought. They basically aimed to fight political machines like Tammany Hall. Regarding Senators, the used to be elected by the state legislature, but in 1914, all Senators started to be elected by direct popular election.