The Progressive Era is a long one, starting roughly in 1865 after the Civil War and lasting until 1921 when Warren G. Harding took over the Presidency and the 17th, 18th and 19th amendments had been added to the Constitution. The areas you include in your question are broad ones, but cover the efforts of the Progressive Era pretty well in my opinion. Building on the above posts, here are some additional thoughts in those three areas:
Big Business: The main effort was against the control of monopolies and trusts, groups of companies that controlled entire industries and could therefore exploit both worker and consumer. In the 1890s, the first real piece of progressive legislation was passed in the Sherman Anti-Trust Act. It wasn't very effective as it was mainly used to break up unions, but it was a step. Later, under Teddy Roosevelt and especially William Howard Taft, the government became more progressive at breaking these trusts apart (Standard Oil, 1912)
Political Rights: The most obvious effort was indeed in the area of womens' voting, and concluded with passage of the 19th amendment. This was a slow effort that built over the entire progressive era, and only became successful with womens' efforts in World War I and Prohibition. States started adopting women's suffrage one by one starting in 1867 with Wyoming, and spreading from there. African-Americans and Native Americans were largely ignored by the Progressive Movement, however.
Social Justice: This was a much bigger challenge for the progressives. Child labor laws, a minimum wage and shorter work weeks were all achieved on their watch, and people like Jane Addams worked tirelessly on behalf of new immigrants, trying to give them a fair shot at life and assimilation with her settlement houses (Hull House, Chicago). Women also led the charge for Prohibition of alcohol in groups like the WCTU and the Anti-Saloon League, citing the widespread social damage to the American family caused by drinking.
What the progressives were trying to do was to reduce the power of big business and of things like political machines. They wanted to return political power to the middle classes -- they saw these as the "best" people.
One of the major things that they did to address the issue of big business was to work against monopolies. They also made the Senate be directly elected because they thought big business was able to pretty much buy senators.
As for political rights, the major thing that they did was to give women the right to vote. They also tried to enhance people's political rights through such things as the secret ballot.
The major thing they did that I would call social justice was to work for better working conditions for the working class. They did things like trying to improve worker safety. I would also put the granting of women's suffrage in here.
With a type of question such as this, I think it's best to use your classroom resources as a reference. Certainly, it's great to incorporate as many avenues as possible. Yet, if you are being assessed on an "exact" sort of answer then I think that you need to make sure that you are following what has been presented in the course. The Progressives really saw themselves as the counter- response to the Industrialists. When Jacob Riis titles his work, "How the Other Half Lives," he is not kidding. Progressives were really driven with this "other half." They addressed issues with this in mind. Big business was addressed in many ways. Progressives attacked the collusion between it and government, and demanded accountability from it in terms of making sure that abuses on the part of business were noted. When Sinclair writes his work, "Oil!", he does so in response to the Teapot Dome scandal and the realities of a government that is in the pocket of big business. At the same time demanding for worker's rights and the ability to collectivize in the forms of unions to ensure that the workers were receiving just treatment and compensation from the "titans of industry" was another way in which Progressives went after industry. Political rights were seen as needing to be expanded, including the voices of previously marginalized groups such as women and African- Americans. The 19th Amendment is a Progressive initiative. The entire movement was driven by a demand for social justice and equality for all Americans. It was a perfect counterresponse to the age of industry that preceded it, demanding a sense of accountability and distribution to the wealth amassed.