In “Nyad,” there are two feats of perseverance on display. First, there is the ceaseless determination of Diana Nyad (Annette Bening) to accomplish a marathon swim from Cuba to Florida across 103 miles of open, shark-infested waters.

This image released by Netflix shows Jodie Foster in a scene from the film “Nyad.” (Kimberley French/Netflix via AP)

In “Nyad,” there are two feats of perseverance on display. First, there is the ceaseless determination of Diana Nyad (Annette Bening) to accomplish a marathon swim from Cuba to Florida across 103 miles of open, shark-infested waters. Then there is the mettle of Nyad’s support team to tolerate the singularly self-absorbed and stubborn Nyad. Both, in the film, are an endurance sport.

“Nyad,” which opens in limited theaters Friday and streams Nov. 3 on Netflix, is in many ways a conventional sports drama, defined by long odds and personal triumph. But there is enough here to help the film, directed by the intrepid filmmakers Elizabeth Chai Vasarhelyi and Jimmy Chin, if not swim against the tide of sports-biopic convention then at least ride a swift current to the finish line.

First and foremost there’s the fact that this is a sports drama led by two actresses in their 60s: Bening and Jodie Foster, who plays Diana’s best friend and personal trainer Bonnie Stoll. When “Nyad” gets underway, the setting isn’t the 1970s, when Nyad’s record swims made her a headline-grabbing sensation. It’s Diana’s 60th birthday, which for her only marks her long distance from a real challenge. “Where’s the excellence?” she says.

Diana soon thereafter gets back in the pool, resolving to complete the Cuba-to-Florida swim, a route some moviegoers may associate more with the Go-Fast boats of Michael Mann’s “Miami Vice” than athletic pursuit. For Diana, the 50-hour endeavor is a matter of completing a long-ago abandoned dream and a way to prove to herself (and everyone else) that age is no match for her will.

It’s the rare role that could be said to be both shark and Oscar bait. Yet Bening’s performance has little vanity to it. Her Diana is obsessively single-minded to the point of unlikeable. When Diana hits the ocean, Bening turns into a ferociously forward-moving force who won’t let anything — not thunder storms, nor jelly fish stings — stop her in her quest. Just keep swimming? She’d leave Dory in the dust.

Diana also comes close to outswimming the people trying hardest to help her. Though the film is principally a showcase for Bening, it’s Foster’s supporting turn that lifts “Nyad.” Foster is a rare screen presence these days, which only makes her warmth and ease all the more powerful here. “Nyad” is balanced between Diana’s admirably insane ambition and Bonnie’s loyal (up to a point) support for her friend. In any case, it’s a reminder, like a pail of cold water, of just how good Foster can be.

Other supporting characters are along for the ride, too, most notably Rhys Ifans’ crusty sea-dog navigator John Bartlett. He’s a cliche but a darn likable one. Nyad has, herself, often been a brash and savvy self-promoter less likely to share the spotlight. It’s to the movie’s credit that it pushes back against its prickly protagonist at the same time it exalts her.

But “Nyad” does accept Nyad’s ultimate accomplishment, even if some have disputed it. Her 2013 swim to the Florida Keys was never ratified by the World Open Water Swimming Assn., and fellow marathon swimmers have cast doubts on it. Nyad has forcefully maintained she completed the swim, without assistance. At times, “Nyad” bends over backwards to depict Nyad as conscientious of the rules.

Vasarhelyi and Chin, in their narrative debut, mix in documentary footage throughout the film, smoothly transitioning from the non-fiction world they come from. They’re the filmmaking team behind documentary standouts like the Oscar-winning “Free Solo” and the Thai cave chronicle “The Rescue.”

Those films were excellent not just due to Vasarhelyi and Chin’s own filmmaking adventurousness but because of their firm grasp of the psychology of those who push themselves to physical extremes. “Nyad” relies on flashbacks to Diana’s past — including an encounter with an unnamed swim coach Nyad said sexually assaulted her and others — to dig into what fuels her.

And just like Alex Honnold of “Free Solo” and the British cave divers of “The Rescue,” “Nyad” convincingly argues that to accomplish something great — to really dream big — you may need a dose of delusion, too.

“Nyad,” a Netflix release is rated PG-13 by the Motion Picture Association for thematic material involving sexual abuse, some strong language and brief partial nudity. Running time: 121 minutes. Three stars out of four.