Elaine Stritch works with musical director Rob Bowman on her one-woman cabaret shows in director Chiemi Karasawa’s documentary “Elaine Stritch: Shoot Me.” (Smart Broad Films)

Longtime fans of Elaine Stritch are more likely to love this documentary portrait of the Broadway legend than are those who only know the actress from her guest spots as Jack Donaghy’s acerbic mother on “30 Rock.” Yet even the uninitiated may find it hard to look away from “Elaine Stritch: Shoot Me,” which, as the title playfully suggests, conveys not only the octogenarian performer’s sardonic fatalism, but also her addiction to attention.

Perhaps most surprisingly, given how easily celebrity is bestowed on the undeserving these days, Stritch earns every second of regard that the film lavishes on her. Even at 86, which is when Chiemi Karasawa’s film starts following her in 2011, the actress is as hardworking as she is charismatic, rushing from rehearsal hall to doctor’s office to bedroom as she outpaces others half her age. It was only last year that Stritch announced her retirement from show biz, shutting down the long-standing series of one-woman cabarets at New York’s Carlyle Hotel that she had performed, with a mix of storytelling and singing, over the past several years.

The film, however, suggests that we may not have heard the last of her.

Though some segments feature sit-down interviews, most of “Shoot Me” is filmed in a fly-on-the-wall style as Stritch goes about her life. Hence, we see Stritch visiting her ophthalmologist, barking orders to an underling to retrieve her dentures and suffering a scary episode of hypoglycemia (she’s diabetic).

But calling it “fly-on-the-wall” isn’t exactly right. Even when she’s not reminiscing directly to the camera about her marriage to actor John Bay, her two dates with John F. Kennedy and her brief love affair with actor Ben Gazzara, Stritch seems acutely aware — and inordinately pleased — that she is being watched. In one amusing sequence, she even directs a cameraman to reshoot her unpacking a box of English muffins.

Stritch is certainly frank, discussing her struggle with alcoholism, as she did in the acclaimed Broadway show “Elaine Stritch at Liberty,” and acknowledging, to a degree, her fears about aging. One thing she is not, however, is self-pitying. Though tinged with sadness, “Shoot Me” is mostly a raucous celebration of Stritch’s great talent as an interpreter of show tunes, which incorporates both the ability to belt out a song to the back of the house and the nuance to make the audience feel as if it’s sitting in on a private musical confession.

Known largely for her work rendering the songs of Stephen Sondheim, Stritch is a great, emotive singer, even if she’s not a technically perfect one. Her voice is rough and raw around the edges.

It is that sense of vulnerability that gives her voice its power. It’s also what makes “Shoot Me” work. Elaine Stritch’s strength, along with the film’s, comes from her honesty. She is herself, even when — maybe especially when — she knows she’s being watched.

★ ★ ★

Unrated. At West End Cinema. Contains obscenity. 81 minutes.

Stritch’s musical director, Rob Bowman, will participate in a Q&A following the 7:20 p.m. screenings on Friday and Saturday.