It’s at this point — of semiretired complacency — that “Nyad” opens, when Diana (portrayed in a salty, vanity-free performance by Annette Bening) is being thrown a 60th birthday party by her best friend, former racquetball champ and personal trainer Bonnie Stoll. Played by Jodie Foster with generous heaps of warmth, humor and humanity, Bonnie puts up with Diana’s bluster and insensitivity even when it hurts. (Diana’s response to the party is to wail, “Where’s the excellence?” instead of saying “Thank you.”) Soon enough, Diana is plotting a comeback of sorts: She will swim from Cuba to Florida, a longtime dream that she is finished deferring. And Bonnie will be her coach.

Directed by Jimmy Chin and Elizabeth Chai Vasarhelyi — making their narrative feature debut after directing “Meru,” “Free Solo” and other documentaries — “Nyad” chronicles the intensive training, failures, internal struggles and breathtaking physical setbacks that Nyad overcame to achieve her goal in 2013, after four grueling (and occasionally life-threatening) attempts. Chin and Vasarhelyi know their way around competition, obsession and the natural world: They do a magnificent job of putting us in Diana’s world, where wind, water, weather and sea creatures take on urgently outsize stakes. If the outcome of “Nyad” is already known — few can forget the news footage of 64-year-old Nyad staggering unsteadily to shore after more than 50 hours in the water — the film manages to build up a surprising degree of suspense, as the filmmakers put the audience in the middle of their heroine’s punishing training regimen; her bouts with seasickness, hallucinations and dreaded box jellyfish; and flashbacks to past traumas that explain not only Nyad’s often off-putting monomania, but her determination to succeed despite nearly impossible odds.

For the past 10 years, Nyad has been a figure of controversy among competitive swimmers, some of whom take issue with whether the Cuba swim was unassisted. (It has not been certified by any organization that governs competitive swimming.) “Nyad” is less interested in those technicalities, or proving Nyad’s detractors wrong, than bearing witness to what was an incredible feat, regardless of the circumstances. As adept as Chin and Vasarhelyi are at re-creating Nyad’s physical experience — the movie is propelled by a soundtrack of songs taken from Nyad’s mental playlist, including vintage classics by Neil Young, Janis Joplin and Simon & Garfunkel — they are even more interested in the human relationships and conflicts at the heart of her quest. Not surprisingly, “Nyad” is a prime showcase for Bening, who delivers a brave, bravura turn as a woman who is frankly not that likable, but whose arrogance and selfishness mask devastating buried wounds. But her characterization would be monotonous and even alienating if it weren’t for a superlative supporting cast, including Rhys Ifans as navigator John Bartlett, a crusty, unsentimental sea dog who can give as good as he gets, and whose knowledge of the Gulf Stream proves crucial, not just to Diana’s completion of the swim, but to her survival.

Ifans is one revelation in “Nyad.” But by far the biggest and most gratifying is Foster, whom generations have watched grow up on-screen, and who here reminds us why she’s among the most beloved actors of her time. “Nyad” sets up an almost too-easy dynamic of the prickly, impatient, self-involved diva and the calm, salt-of-the-earth bestie who makes her relatable to the outside world. But Foster takes that otherwise simplistic equation and makes it something deeper, more subtle and ultimately more moving.

Diana may be the star of “Nyad,” but Bonnie is the film’s heart and soul, thanks to Foster’s quiet, unshowy instincts and magnetic screen charisma, which dazzles even when she’s dressed down in baggy cargo shorts and dorky shades. Would it be a betrayal of the movie’s feminist cred to say she’s just plain gorgeous? Who cares? Despite its over-credulous willingness to go along on what through one lens amounts to a massive ego trip, “Nyad” manages to be a celebration of perseverance, self-belief and learning how to be loved. It’s also about aging gracefully, and a little crankily, on and off the screen. Viva the divas, in all their shapes, sizes and temperaments, and however they care to be defined. “Nyad” is here for it — sharks, stingers and haters be damned.

PG-13. At Landmark’s E Street and Bethesda Row cinemas; available Nov. 3 on Netflix. Contains mature thematic material involving sexual abuse, some strong language and brief partial nudity. 120 minutes.