Movie stars shine. It's their job. But given the right role, the best of them face the camera with all glamour stripped away. It takes guts as well as talent but there are consolations and an Oscar can be one of them – as Julianne Moore found this year after her performance in Still Alice as a sufferer of early-onset Alzheimer's disease.

In Freeheld, she's in trouble again, stricken this time with cancer. The film is an adaptation of an Oscar-winning documentary about a lesbian couple – New Jersey detective Laurel Hester and her partner, Stacie Andree – who mounted a campaign in 2005 to have Hester's police pension go to Andree after her death. Since Hester had already been diagnosed with terminal lung cancer, their need was urgent.

The grim rituals of the disease and its treatments have become all too familiar on screen. Even so, the sense of dread they evoke is as potent as ever. And here, there's no attempt to cover up either its ravages or the side-effects of a harsh chemotherapy regimen. Bald, hollow-eyed and struggling for breath, Moore charts Hester's physical disintegration with brutal candour while, at the same time, conjuring up the indomitability of somebody determined to leave a worthwhile legacy – to her partner and to other gay couples caught in the same bind.

When she and Stacie (Ellen Page) set up house together, Hester still hasn't come out to her fellow policemen. She's ambitious and being a female cop is difficult enough. If it's known that she's homosexual, as well, she believes that her chances of promotion will shrink to zero. Her partner on the force, Dane Wells, is the first to find out and he becomes her fiercest advocate when her pension request is refused.

He's played by Michael Shannon, who has a square jaw, a steely look and a reputation for playing heavies but makes an effortless transition to being a good guy. His is a quietly effective presence, radiating kindness and gravitas in counterpoint to a wildly ebullient Steve Carell as a gay activist whose preferred weapon is a crowd chanting slogans at full volume.

Hester and Andree, who is 18 years younger, are also quiet people. Their house is in the suburbs with a garden and a dog, and Moore and Page, who is gay, do their best to get comfortable together but somehow it never happens. The script by Ron Nyswaner (Philadelphia) is partly to blame. The early scenes, which have the couple meeting and falling in love, lapse into cliche. It's not until Hester is desperately ill that you sense real tenderness and intimacy. Even so, it's their courtroom battle – and Moore's uncompromising performance – that give the film its charge.