Of American-English origin, the expression Montezuma’s Revenge (also Montezuma’s revenge, Montezuma Revenge, Montezuma revenge, Moctezuma’s Revenge, etc.) denotes diarrhoea suffered by travellers, especially in Mexico.
—Synonyms: Pharaoh’s Revenge and gyppy tummy.

The expression Montezuma’s revenge occurs, for example, in The trouble with travelling, by Dr. Abraham Marcus, Medical Correspondent, published in The Observer (London, England) of Sunday 17^th June 1962:

YOU call it Turista, Montezuma’s revenge or the Aztec two-step if you are an American—or Casablanca crud, perhaps; more likely Delhi belly or Gyppy tummy if you are British. Doctors call it the diarrhoea of travellers.
It occurs all over the world. The Greeks probably have a word for it, too—it is not confined to the superior Anglo-Saxon exposed to a doubtful Mediterranean hygiene.

William Rowell explained the expression Montezuma’s Revenge in his column, Rowell’s Words, published in The Jessamine Journal (Nicholasville, Kentucky, USA) of Thursday 17^th February 2022:

We all know the story about “Montezuma’s Revenge”. He was the ruler of the Aztec nation in South America. It was invaded and came under control of an invading Spanish army. He was captured by the Spaniards and died, some say murdered, while held under their confinement. *
Since then, tourist [sic] to Latin American countries that drink the water have been subjected to diarrhea as his revenge.

[* The last ruler of the Aztec empire in Mexico, Montezuma II (c.1466-1520) was defeated and imprisoned by the Spanish in 1519. He was wounded by some of his former subjects while trying to pacify them during an uprising against his captors, and died several days later, either from his wounds or at the hands of the Spanish.]

The earliest occurrences of the expression Montezuma’s Revenge (also Moctezuma’s Revenge) that I have found are as follows, in chronological order:

1-: From a letter that Daniel Laban Beebe (1887-1973), editor and publisher of the Oroville Mercury (Oroville, California, USA), wrote from Panama City on Tuesday 4^th October 1955—letter published in that newspaper on Wednesday 12^th October 1955:

I’ve felt fine so far. I learned during the trip to Mexico nine years ago what to eat and what not to eat. Several of our party would not observe the warnings of more experienced members, and have been down already with what is jokingly called the Aztec Two-step, or Montezuma’s Revenge. It is no joke, however.

2-: From the column It Happened Last Night, by the U.S. journalist and gossip columnist Earl Wilson (1907-1987), published in several U.S. newspapers in November 1955—for example in the Courier-Post (Camden, New Jersey, USA) of Monday the 7^th:

The crew of Warner Bros’. “Serenade,” most of whom got sick on location in Mexico, call their stomach ailment “Montezuma’s Revenge.”

3-: From Reaper Rat Race, by ‘Mighty Mouse’, published in The Richfield Reaper (Richfield, Utah, USA) of Thursday 10^th November 1955:

He did prepare for just about any medical emergency by taking along a formidable supply of remedies, including one for an intestinal disorder that afflicts all foreigners immediately upon crossing the border into Mexico. This distressing malady, according to Norm, is known simply as “Montezuma’s Revenge.”

4-: From Matt Weinstock’s column, published in the Mirror-News (Los Angeles, California, USA) of Wednesday 23^rd November 1955—Matt Weinstock (1903-1970) was a U.S. journalist, newspaper editor and columnist:

GRINGOS visiting Mexico who worry about “Montezuma’s Revenge” may profit by this advice from the Mexican Association of Travel Agencies:
“Enchiladas are tortillas rolled up with a lot of different things, either individually or collectively, inside. If the tourist is eating enchiladas in a high class restaurant, he doesn’t need to worry. If he’s eating enchiladas in a cheap dump, well, why not live with abandon?”

5-: From the column Our Town, by the Canadian journalist, newspaper editor and columnist Jack Scott (1915-1980), published in The Vancouver Sun (Vancouver, British Columbia, Canada) of Thursday 19^th January 1956:

Manuel Guerrero, a theatrically handsome young doctor, who treated me last winter in Acapulco for the tourist trouble known as Montezuma’s Revenge or the Aztec Two-Step, has written me that the recent series of earthquakes in the resort was enjoyed by all.

6-: From John England’s For Men, published in the Valley Times (North Hollywood, California, USA) of Monday 20^th February 1956:

Should you be planning a vacation in tropical Acapulco this season (average high, 83, average low, 68) here are some dress tips:
[…]
Acapulco is essentially a casual resort but this doesn’t mean sloppy dress. Well coordinated, colorful outfits are carefully selected by well groomed men seen around the better hotels and entertainment areas.
And don’t forget your favorite sun tan lotion—it may not be available in Mexico—sun glasses and whatever your doctor suggests for Moctezuma’s Revenge, a factor which must be considered even though you limit liquid intake to beer and taquilla.

7 & 8-: From the column Looking Sideways, by the U.S. screenwriter, theatre critic and columnist Whitney Bolton (1900-1969), published:

7-: In the Fort Myers News-Press (Fort Myers, Florida, USA) of Wednesday 15^th August 1956:

QUERETARO, MEXICO—
Among the ways not to visit Queretaro is on a day when cliffs alongside the main highway between Toluca and this gem-studded city are being dynamited with a resulting accumulation of large rocks on the road. A second complication could be a young girl who suddenly and without warning begins to run a fever of 102 because of an attack of an ailment delicately known as Montezuma’s Revenge.

8-: In the Okmulgee Daily Times (Okmulgee, Oklahoma, USA) of Thursday 16^th August 1956:

QUERETARO, Mexico—Among the ways not to visit Queretaro is on a day when cliffs alongside the main highway between Toluca and this gem-studded city are being dynamited with a resulting accumulation of large rocks on the road. A second complication could be a young girl who suddenly and without warning begins to run a fever of 102 because of an attack of an ailment delicately known as Moctezuma’s Revenge.

9-: From the column Behind the Mike, by ‘B. Mike’, published in The Oregonian (Portland, Oregon, USA) of Wednesday 21^st November 1956:

AFTER A FEW DAYS in Mexico City, most Norteamericanos come down with a rather distressing tourist ailment, known under various names such as “Aztec Toothache,” “Montezuma’s Revenge,” “Aztec Twostep.” You can watch them, pale and drawn, wandering in and out of the exclusive shops along Paseo de la Reporma, or ducking over to the drug store at Sanborn’s for pills. Tourists are divided into three groups over best way to stay healthy in Mexico. One school of thought holds that the turista should avoid all unbottled water, fresh fruits or vegetables that can’t be peeled (no lettuce salad, tomatoes). A second claims that you’ll get sick anyway, so why not enjoy all the food and drink that comes along. Just be sure you have a bottle of sulfasuxiadine or Entero Vioformo in your pocket. Third school takes a position somewhere between the first two. These gents take all the precautions, but brush teeth in tap water and gulp down rum collins containing ice cubes made from tap water.
MOST TOURISTS SUSPECT that hotel bought large bottle of mineral water several years ago which maid refills fresh from tap each morning. When mineral water isn’t available, some extremists brush teeth in Coca Cola (this has distinctive flavor and it’s a wonder someone hasn’t brought out a Coca Cola toothpaste in the states). Aztec Toothache lasts a horrible three hours if you start gulping sulfasuxiadine pills when you feel first symptoms, but goes along for several days if allowed to run its normal course. On previous trips, I’ve always followed first school of thought on food and drink, and become ill. This time I ate and drank anything that came along except the vile-smelling coffee—and felt fine.