Pushing one’s body to the limit, seizing every ounce of courage and endurance deep within, and going even farther to overcome the odds and reach an almost impossible dream. Diana Nyad’s story of her swim from Cuba to Florida at age 64 is the stuff that biopic dreams are made of. Directed by documentarians Elizabeth Chai Vasarhelyi and Jimmy Chin (“Free Solo”), “Nyad” is a film that seeks to win over the hearts of its audience through the astonishing true tale of one woman’s unflinching determination.

Biopics are known to sometimes take something humanly powerful and turn it into a maudlin formula. Written by Julia Cox, “Nyad” doesn’t try to sidestep the cliches that come with this type of film, but achieves something quite rare as it makes every moment feel unforced and organic.

A tremendous Annette Bening is endurance swimmer Diane Nyad, a woman who is the definition of resolve. Diane seeks to complete her lifelong dream of completing a record-breaking swim from Florida to Cuba. After an unsuccessful attempt in her twenties, Nyad (in her sixties) tried again. The picture begins with real-life footage of Diane Nyad through newscasts and talk shows; the reverse of how most films do it, revealing the actual subjects at the end. Diana is rather antisocial and misses her time in the world of sports, reporting for the 1970s program, “The Wide World of Sports. She is a woman who fails to sit by and let the world tell her (and all women) that reaching your sixties means giving up on unachieved goals. Nyad’s personality is often abrasive, keeping her at a distance from almost everyone.

Best friend and eventual coach, Bonnie Stoll (Jodie Foster), shares her days and nights with Diana. Theirs is an unbreakable bond, as the two women (once lovers) have a settled in relationship. Diana and Bonnie may no longer be an official couple, but they certainly exist as one. Bening and Foster are magic, elevating a semi-standard sports-bio into something quite exhilarating; their performances enlivening an already inspiring film. The two actresses capture the emotion of the piece and the soul of their characters without resorting to mawkishness.

Bonnie is a bright light and Foster inhabits the role with a resilient sensitivity that is as intoxicating as it is moving. This wonderful actress has never been so exquisitely natural in what is one of the finest performances of her career.

Annette Bening is beyond committed to capturing not only Diana Nyad’s will-power, but the physical and mental pain she goes through when all seems lost. Bening doesn’t gloss up Diana in the physical nor the emotional, going without makeup and really becoming her real life character through a committed physicality. It is incredible work from one of our very best.

As Diana and Bonnie prepare for the training (and eventually the big swim), the film goes through the standard training moments, but the directors intersperse them with more actual footage of their subject. Listening to the real Diana Nyad speak to the demands of preparing her body and mind heighten the intensity of watching Bening and Foster muster through these scenes.