What were John Tyler's major accomplishments?

John Tyler was the first vice president to ascend to the presidency upon the death of the incumbent. As such, he established precedents that served to assure the legitimacy of future presidents who attained the office in such manner. Though Tyler's insistence that he was not merely an acting president but the president in fact was not entirely accepted during his administration, in time this became a noncontroversial mainstream view.
Tyler's primary accomplishment as President was working to bring Texas, which had achieved independence from Mexico in 1836, into the United States as the 28th state. Tyler's own unpopularity with Congress prevented the annexation of Texas from taking place until the very end of his term.
Tyler had been elected as a member of the Whig Party, but once president, he quickly found himself in opposition to many of the priorities of congressional Whigs, particularly the establishment of a national bank. As a result, he was in essence expelled from the party and served out the majority of his term without any real allies in Congress. His constant squabbles with Congress, which included a brief attempt at impeachment, helped to establish the conventional wisdom that a president could not realistically thrive in office apart from association with one of the major parties.

John Tyler is generally not regarded by history as a very successful or noteworthy president, but he can nonetheless be credited with a number of not inconsiderable accomplishments.
His accomplishments, detailed below, might be considered especially impressive given that he was not expecting to become president. He only took the office when the serving president, President William Henry Harrison, died unexpectedly in 1841. John Tyler then held the office of president (as the tenth man to do so) until 1845.
Perhaps President Tyler's first major accomplishment was the 1842 Webster-Ashburton Treaty with Great Britain. This treaty successfully settled a number of border disputes between the United States and British colonies to the north.
President Tyler's second major accomplishment was arguably the 1844 Treaty of Wanghia. This treaty made it possible for America to trade in Chinese ports on the same level—and with the same benefits—as Great Britain.
A third significant accomplishment of Tyler's presidency was the annexation of Texas in 1845. The annexation bill was signed by Tyler during his last days as president.