Short answers, pulled from the story.
Oppenheimer earned the title because he served as director of the Manhattan Project's Los Alamos Laboratory from 1943, overseeing the scientific development that produced the first nuclear weapons. He assembled the team, directed both theoretical and experimental work, and was present at the Trinity test on the 16th of July, 1945, the first successful detonation of a nuclear device.
Oppenheimer's brother Frank recalled his first words as "I guess it worked." According to a 1949 magazine profile, Oppenheimer thought of lines from the Bhagavad Gita at the moment of the explosion: "Now I am become Death, the shatterer of worlds." In 1965 he recalled that most of those watching were silent.
A 1954 AEC hearing revoked Oppenheimer's security clearance by a 2-1 vote, citing his past associations with Communist Party members and his opposition to developing the hydrogen bomb. The board unanimously cleared him of disloyalty but found 20 of 24 charges true or substantially true. The decision was vacated by the U.S. Department of Energy in 2022.
Oppenheimer co-authored the Born-Oppenheimer approximation for molecular wave functions, predicted the existence of positrons in 1930, and co-wrote a 1939 paper with Hartland Snyder predicting what became known as black holes. He also developed the Oppenheimer-Phillips process in nuclear fusion with Melba Phillips, and his student Willis Lamb won the 1955 Nobel Prize for work Oppenheimer had anticipated in a 1931 paper.
Oppenheimer learned Sanskrit under Arthur W. Ryder at Berkeley in 1933 and eventually read the Bhagavad Gita in the original text. He called it "the most beautiful philosophical song existing in any known tongue," gave copies to friends, and kept a worn personal copy on his desk at Los Alamos. He quoted from it at President Franklin Roosevelt's Los Alamos memorial service.
Oppenheimer was nominated for the Nobel Prize in Physics four times, in 1946, 1951, 1955, and 1967, but never won. Some physicists and historians have since suggested his work on gravitational collapse and the theory of neutron stars and black holes may have been his most important contribution, though it was not recognized by the Nobel committee during his lifetime.