How did Theodore Roosevelt's foreign policy differ from previous Presidents?

If we're looking all the way back to the beginning of the country (and the long term history of the United States), I would say that there was a radical shift in foreign policy at the end of the nineteenth century (and the beginning of the twentieth), when the United States turned more aggressively imperialistic in terms of overseas expansion, and that Theodore Roosevelt played a critical role in that transition, pushing the United States even further down the path of empire.

Some of his foreign policy interventions include building the Panama Canal (and to ensure that he could build the canal, he sent military forces to intervene in Panama's revolution against Colombia), mediating peace talks between Russia and Japan, and invoking the Roosevelt Corollary to the Monroe Doctrine. In conclusion, Roosevelt oversaw an active and aggressive brand of American imperialism.

The major difference between Theodore Roosevelt and his more recent predecessors in the White House was that his foreign policy was much more aggressive.  This was the era of the “big stick” in which the US asserted its power around the world, and particularly in the Caribbean.  However, it is not clear if this is really a change that comes about because of Roosevelt or because of a change in the country’s circumstances.

By 1901 when McKinley was killed and Roosevelt took office, the US was much stronger than it had been in the past.  Industrialization had built its capacity to do things like building ships.  Alfred Thayer Mahan’s doctrines had been accepted by many Americans and the US Navy was larger and more powerful than in the past.  The US had been getting more aggressive, as seen in things such as the the annexation of Hawaii and the Spanish-American War.

This meshed perfectly with Roosevelt’s own inclinations.  He was inclined to follow a foreign policy that explicitly sought to increase American power.  He was more aggressive in pursuing American power around the globe than previous presidents had been.

What were the main achievements of Theodore Roosevelt's foreign policy?

Because your other questions have been about the early 1900s (or earlier) I am assuming that you are asking about the first President Roosevelt.  I have edited and moved your question to reflect this.

Theodore Roosevelt had a number of major foreign policy initiatives and actions during his time as president.  Some might argue that not all of these should be called achievements.  These included:

• Establishing the United States as a relatively important world power.  This can be seen in at least two ways.  One was the Roosevelt Corollary to the Monroe Doctrine.  Here, Roosevelt asserted the right of the US to intervene in the domestic affairs of any nation in the Americas to prevent European interference.  The second was the sending of the "Great White Fleet" to show American power around the world.
• The beginning of the Panama Canal.  Under Roosevelt, the US helped (in somewhat dubious circumstances) Panama become independent of Colombia.  The US then negotiated a treaty for a canal zone and started work on that canal.
• The Russo-Japanese War.  President Roosevelt brokered a peace treaty between Russia and Japan in 1905.  He won the Nobel Peace Prize for his efforts.

These are the most important events (that could be called achievements) in Roosevelt's presidency.