She did not get anything by claiming to be native American. She is a tenacious, passionate, and intelligent critic and opponent to the current administration and these attacks on her are their response, similar to Trump's absurd and repeated claims that President Obama was not born in the US.
Here is an excerpt from the Snopes report on her Harvard job appointment:
"In the most exhaustive review undertaken of Elizabeth Warren’s professional history, the Globe found clear evidence, in documents and interviews, that her claim to Native American ethnicity was never considered by the Harvard Law faculty, which voted resoundingly to hire her, or by those who hired her to four prior positions at other law schools. At every step of her remarkable rise in the legal profession, the people responsible for hiring her saw her as a white woman.
The Globe examined hundreds of documents, many of them never before available, and reached out to all 52 of the law professors who are still living and were eligible to be in [on the decision]. Some are Warren’s allies. Others are not. Thirty-one agreed to talk to the Globe — including the law professor who was, at the time, in charge of recruiting minority faculty. Most said they were unaware of her claims to Native American heritage and all but one of the 31 said those claims were not discussed as part of her hire. One professor told the Globe he is unsure whether her heritage came up, but is certain that, if it did, it had no bearing on his vote on Warren’s appointment."