This was one of my favorite biographies last year. I actually first heard about the book in October 2015 when a scathing review was published in the New York Review of Books (the gist of that review, as I remember it, was that Didion wants to be left alone and so the biographer should have dropped the topic, which is a curious argument to make of a public figure, although it is indeed unfortunate that Didion or her close friends and associates didn't make themselves available for interviews). I remember feeling sorry for the biographer that his book wasn't apparently judged on its merits in the NYRB - at the time I had no idea I would switch jobs and move to SMU, which the author graduated from, but it was a fun coincidence when I found out. The NYRB review didn't hurt the sales, apparently, since the book became a New York Times bestseller.
Except for a few moments when the author seems a little too keen in discussing the troubles affecting Quintana Roo (Didion's adoptive daughter who died at 39 in 2005, shortly after Didion's husband passed away), the book seemed unflinchingly thoughtful, fair and completely uninterested in gossip, with a focus on Didion herself rather than an analysis of her writings. Didion is an interesting character, who has lived both on the East and West Coasts and has become a legend in the literary world (although her earlier books such as The White Album are infinitely better than her more recent ones like The Year Of Magical Thinking, in my opinion). The Last Love Song manages the feat of showing us how Joan Didion became Joan Didion.
For a complementary perspective on Didion as a writer, her 1977 Paris Review interview is a good start. She was also the subject of a 2017 Netflix documentary, discussed in this New Yorker piece.