Why did President Lyndon Johnson's major domestic achievements come to be overshadowed?
The major reason for this was the Vietnam War. When the Vietnam War started going badly, it overshadowed all of Johnson's other actions and led him to decide not to even run for reelection in 1968.
By the time that the 1968 election came around, the war in Vietnam had become very unpopular. This came to a head in early 1968 when the Tet Offensive made it clear that the government had not been completely open with the people as to how the war was going. At that point, it seemed clear to most Americans that the war was not on the brink of being won. This disillusioned many Americans about the war and about Johnson.
The social strife caused by the war, along with the economic and human costs of the war, overshadowed Johnson's domestic achievements.