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.