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Of American-English origin, the alliterative expression bikini body designates the type of body, typically slim and shapely, conventionally considered to look attractive in a bikini.

By synecdoche, this expression has come to also designate a woman whose body is of that type—cf., below, quotations 5 & 7.

The expression bikini body has been criticised in particular for the promotion of an unrealistic body image—as mentioned, for example, in the following from the Irish Independent (Dublin, County Dublin, Ireland) of Wednesday 7^th September 2016 [page 27, column 4]:

You say bikini, they say burkini. I say it’s nobody’s business what women wear
Lorraine Courtney

Do you think what you wear on the beach is your own business? You’re wrong. But if the burkini is the sign of a repressive society, then what is the body-shaming reaction of Western society to the body of a woman in a bikini, deciding if she’s ‘beach ready’ or not? At the heart of both stories is the same unhealthy obsession with women’s bodies and how they should or shouldn’t be displayed.
This summer was the 70^th anniversary of the bikini. The two-piece was launched in France in 1946 by engineer Louis Réard; this was also the summer the bikini died. Loads of retailers are reporting plunging bikini sales and a rise in sales for one-piece swimsuits instead. […] For years, the bikini body was a tyranny we couldn’t get away from, but it appears that we’ve finally had enough of the ‘beach body’ shaming and are covering up instead.

These are, in chronological order, the earliest occurrences of the expression bikini body that I have found:

1-: From the following advertisement for Slenderella International, a chain of weight-loss salons, published in Newsday (Hempstead, New York, USA) of Monday 12^th June 1961 [page 33, column 2]:

FOR SUMMER FUN AT SLENDERELLA
LOSE THAT FAT FLABBY DROOPY BODY!

SUMMER’S WONDERFUL FUN is for those who look young. High firm bust—hand span waist—trim, firm hips—slender graceful legs—a Bikini body!

The following image illustrated the advertisement for Slenderella International published in Newsday (Hempstead, New York, USA) of Monday 12^th June 1961 [page 33]:

2-: From Europe by Scooter (Manila (Philippines): Erehwon, 1965), by Antonio C. Abaya [page 38]:

The company was gay and colorful. We had, among other things, an FLN * rebel from Algeria, a hunchback from Notre Dame, a penniless German blonde, with straight Nordic hair and a perfect bikini body, who was really going to try to make the scene at St. Tropez, an American from Harvard on his way to study theoretical physics in India, and a pair of Canadian girls doing the continent on a scooter.

* FLN stands for Front de Libération Nationale (i.e., National Liberation Front), the main nationalist movement during the Algerian War of Independence (1954-62).

3-: From the column Petticoat Chatter, by Bea Rosenberry, published in the Pottstown Mercury (Pottstown, Pennsylvania, USA) of Wednesday 12^th May 1965 [Woman’s Page, page 17, column 8]:

In doing the legwork for you readers, I’ve opened a lot of doors and I’ve made some delightful discoveries. Holland-Moritz is one of them. […] A larger variety of styles and sizes than any in the area. A jolly jolt of colors appears in some of the swimsuits where there can be less suit and more you, if you prefer. Whatever your size, a small, modern bikini body or one curvaceously full, you can find something to bring out your own “youness”, that femaleness that is yours alone.

4-: From The G.H.S. Advocate, Greenville High School’s student magazine, published in the Greenville Advocate (Greenville, Ohio, USA) of Saturday 14^th May 1966 [page 2, column 2]:

Diet, Exercise For Bikini Body
By Christine Mote

Now that summer is approaching rapidly, the time has come for the traditional spring improvement course. There are three main areas to cover; the first and most important is “the bikini body”.
How many of you girls could honestly slip into a swimming suit right now and be pleased with your appearance? Ah ha! Not many I see! Don’t fret; I will help you.

5-: From From Beach Movie Blitz To Absurd Adventures, by Sara Davidson, published in the Boston Sunday Globe (Boston, Massachusetts, USA) of Sunday 17^th July 1966 [page 18—A, column 1]:

When the first beach flick, “Bikini Beach,” came out in 1964, it established a world set apart, with characters and laws of behavior all its own. It was […] a community and it was the teens’ own.
[…]
[…] The films won young fans in droves. Each new beach movie featured the same actors in the same roles. Even the chorus line of bikini bodies was kept intact.

6-: From The Plain Dealer (Cleveland, Ohio, USA) of Sunday 16^th October 1966 [Section H, page 1, column 1]:

Angel face, bikini size hath Judith McCauley
By Peter Bellamy

Judith McCauley is a young lady from Marietta with the face of an angel, a bikini body, a warm, throbbing, true coloratura soprano voice and a great future.
Her lovely voice has theater goers talking to themselves as she performs in the musical comedy, “The Desert Song,” which opens its second week at the Hanna Theater tomorrow night.

7-: From a review of Don’t Make Waves (1967), a sex-comedy film starring Tony Curtis, Sharon Tate, Claudia Cardinale and Dave Draper—review by Patrick Gibbs, published in The Daily Telegraph and Morning Post (London, England) of Friday 4^th August 1967 [page 17, column 3]:

Mr. Curtis’s idea of using a beautiful bikini body (Sharon Tate) to publicise the swimming pools by sky-diving into one, and the necessity of getting her away from her fiancé—a Mr. Muscle—provide a few funny moments.