This image released by Hulu shows Andra Day in “The United States vs Billie Holiday.”

Billie Holiday has always been a monster of a role. Diana Ross tackled her on film and Audra McDonald did it on stage. Now it’s time for Andra Day — a singer and actress perfectly named to play Lady Day — and she shines. It’s a pity the film she’s in is so messy.

In the frustrating “The United States vs. Billie Holiday,” Day gives it her all as Holiday, but she can’t save a film that is overstuffed yet also thin. Director Lee Daniels and screenwriter Suzan-Lori Parks offer an unfocused, meandering work for much of the time.

Day plays Holiday in the last years of her life as a haunted and crushed icon, an addict with terrible choices in men but the voice of an angel. Day’s body is angular and lean and seemingly always prepared for blows to rain down, a piece of gum and a cigarette ever-present in her mouth. But she is also liable to punch back and rip into anyone crossing her. It is a remarkable performance, not least because it is Day’s first acting role.

Daniels and Park have chosen as their skeleton an unlikely love affair between Holiday and Jimmy Fletcher, a Black federal agent ordered to infiltrate her group and get her arrested for using heroin. Why? Because whites cannot stand her singing the anti-lynching song “Strange Fruit.”

A film that desperately needs to be taut is anything but, making space for over-the-top dog funerals, distractions like Roy Cohn and Holiday’s friendship with Tallulah Bankhead. And yet there are moments of brilliance, as when Jimmy takes heroin and Lady Day appears in the haze of his high as a child to take him for a flashback to the whorehouse she spent time in as a youth. It is a fascinating technique but quickly abandoned.

The best parts are listening to Day as her Holiday sings onstage — perfectly put together with a red lip and a big blossom over her right ear — and watches the men in her life sit at lounge tables and determine her fate. Sometimes her gowns hid cracked ribs. “She look like a million bucks but she feels like nothing,” we are told.

The film’s clear climax is a scene in which Holiday stumbles on a rural family after a lynching and it is searing, anguishing and horrific, images that will stay with the viewer as much as they fueled Holiday’s need to sing “Strange Fruit” despite the risks to her career.