Question

what was the goal of trust-busting in the early 1900s

Answer 1

I believe that the most fitting answer for this question would be prosecuting "trusts," or monopolies, that were in violation of the federal Anti-Trust law. During the Progressive Era, or 1900 to 1917, trust-busting efforts were very prevalent. Roosevelt, Taft, and Wilson were especially adamant about trust-busting. Hope this helps.

Answer 2

The gold of the trust-busting in the early 1900s was eliminate or regulate those business, which due to their increasing fraudulent actions like intimidation and bribing,  were  becoming and impediment to a free market economy.

Monopolies and Trusts became the principal target for then President Theodore Roosevelt between 1901 and 1909. But the fight against these entities continue until 1917. The previous approach from the government to stay away from big businesses, was no longer effective because these big monopolies were using their corporate power to abuse smaller businesses.  

President Roosevelt was very clear and conveyed that he was not against big businesses and Trusts, only those who were abusive and bad for a free market economy.

Federal regulation of big  businesses was extremely difficult to implement but at the end, new anti-trust laws and regulations were created, to keep this corporations within the law.