In The Brief Wondrous Life of Oscar Wao, I'm not sure that Oscar achieves the American dream himself, but I do think that Oscar helps Yunior and Lola to achieve it.
The American dream is, at its height, a belief that one can go from rags to riches almost overnight. More realistically, however, it is the simple hope that each generation will have it better than the one before. Early in Oscar's life, he hopes for the former fantasy: he wanted love (or at least sex) and artistic fame (to be a Latino Tolkien). When it doesn't happen, he gets fat--orca fat. It is not until his last year did Oscar realize the latter: that by becoming a martyr for the fuku can he give Lola a chance at love and Yunior a chance at becoming an artist.
Throughout the novel, Oscar slowly moves from fantasy to reality, and his depiction of the American dream follows suit. Finally, he realizes that, by going to the Dominican Republic and doggedly confronting his family history and pursuing love, can he end generations of suffering at the hands of the fuku. As a result, Oscar's death helps Lola to marry, have a daughter, and escape the fate of Belli. Thanks to Oscar, no longer is Lola the victim of sexism and male dominance. Likewise, Oscar's death haunts Yunior to achieve his literary potential; he takes over where Oscar left off: by teaching and writing. So says eNotes:
Yunior is haunted by dreams of Oscar until he decides to clean up his life. Yunior decides to teach college and get married, declaring himself "a new man" and that he "learned that from Oscar."
Ironically, the achievement of the American dream is the very publication of the novel itself, for Junot Diaz (very much a ghetto nerd like Oscar and a meathead like Yunior) was able to be saved from the streets by education (attending Rutgers) and language (writing Latino and fantasy-infused fiction).