If Tilda Cobham-Hervey’s lively-eyed portrayal of Reddy is accurate, I bet the 78-year-old entertainer is getting a kick out of the raunchy ode to women’s pleasure. What really bugged Reddy were sad-sack songs like 1966’s hit “Born a Woman” — “A woman’s place in this old world/Is under some man’s thumb…”

The Australian singer became a household name in 1972, when her fiery first single “I Am Woman” hit at just the right time to galvanize the women’s movement, which was advocating for the Equal Rights Amendment. The film often looks and sounds like an accompaniment to the Cate Blanchett-led Hulu series “Mrs. America”, though plot-wise it stays mostly in genre territory, never wandering very far into the cultural waves Reddy created when she sang about the struggle for equality.

Cobham-Hervey (“Hotel Mumbai”), 26, brings great presence to the role, though. We meet Reddy as a young single mom in New York, frustrated at her inability to break through the “male groups are all the rage” bluster at record companies, and living in a fleabag hotel. Meeting the mildly greasy William Morris agent Jeff Wald (Evan Peters, 33) helps get her foot in the door. It’s fun to watch a table of male music execs squirm as they listen to her song: Too angry, they say. But they’re still unable to turn down all the potential cash to be made off of her feminist fan base.

Danielle Macdonald (“Dumplin’”), 29, is a highlight as Reddy’s Aussie friend Lillian Roxon, a rock journalist who encourages Reddy not to give up on her dreams. But she’s left behind when Reddy and Wald move to LA, trapping the singer in a lonely domestic existence while her husband is purportedly trying to get her a record deal.

Director Unjoo Moon (“The Zen of Bennett”), 56, is at her best showcasing the circumstances that galvanized Reddy to push relentlessly to be seen and heard. But some of the film’s most climactic moments feel a little pat — Reddy singing “I Am Woman” to a live audience for the first time, the gradual smiles and head-nodding amongst the women in the crowd. Or the increasingly frequent shots of her sweaty husband hoovering up lines of coke.

I’d have been curious to see more about Reddy’s interactions with the women’s movement, but the film mostly has room for this one woman. Thanks to Cobham-Hervey’s performance, it’s an engaging, if fairly familiar, story.