Renée Zellweger keeps saying “Judy” is a “love letter” to Judy Garland, and for once, the P.R. blather is legit.

“Judy” doesn’t sugarcoat the failings of the legendary entertainer from Grand Rapids, Minn., who is depicted during the final concert engagement of a life that ended at 47. But it’s a loving effort to understand where things went wrong, why her kids insist she was a marvelous mother, and how come fans loved the icon so deeply that for years her death was listed as a trigger of the Stonewall Riots — which launched the gay rights movement the day after her funeral.

“Judy” shows its fragile title character, held together by pills and mascara, agreeing to a run of concerts in London. She says she can’t get work in America because, “I’m unreliable and uninsurable. That’s what the ones who like me say to my face.” But her reputation for showing up drunk and skipping shows apparently hadn’t made it to London in 1969, and, desperate for money to support her two youngest children, she goes on. Soon, Brits know all about her showing up drunk and skipping shows.

It’s widely agreed that the problem was the uppers and downers Garland used to get through the day, a habit “Judy” depicts (in poorly directed flashbacks) as beginning during the filming of “The Wizard of Oz” more than three decades earlier. Teenage Judy is told she’s worthless by Louis B. Mayer (Richard Cordery is not credited on the film’s IMDb.com page, possibly because he gives what could end up being the year’s worst film performance). She’s also hounded by a studio minion who pulls food out of one side of her mouth while inserting sleeping pills in the other. Judy’s insecurities, paired with dependencies on drugs and booze, followed her until she died.

Egad, that makes “Judy” sound like a — you should pardon the expression — downer. It is sad, but it’s not grim because Zellweger’s utterly convincing performance shows that Judy was hilarious, self-deprecating, an affectionate mom and a loyal friend. In one revealing, albeit fictitious, sequence Judy meets a couple at the stage door and spends an evening with them, making scrambled eggs and playing cards. Performing seems painful for her at this stage of her career, but in those offstage hours, she allows herself a few moments of relaxed joy.

Wiry and wearing brown contacts that make her eyes look a lot like Garland’s, Zellweger — who has shed the adorable face-crinkling she often relies on — captures the essence of Garland with stabby hand gestures and raspy inflections. She looks more like the Garland of “A Star is Born” than the late-in-life version. But she does resemble her, and although the actor’s perfectly fine singing doesn’t sound like Judy, it captures the loneliness and neediness of a performer who gave everything she had for as long as she possibly could. Zellweger’s dancing is excellent, particularly in “The Trolley Song” that appears so second nature that you believe it’s based on 25 years of muscle memory.

Maybe the movie is informed by the fact that Zellweger also is in comeback mode, having not made a decent movie in — what, more than a decade? She’s great throughout “Judy,” but she’s best in unguarded moments such as one that creates the illusion of being captured on the fly: Bleary-eyed, drugged up and late for her opening-night performance, Judy is hustled into an elevator and, as the elevator doors close, the last thing we see is her assistant schlepping on her earrings. It’s Judy Garland, human, transforming into Judy Garland, superstar, and it shows how incredibly difficult it was to be both.