This was an old English language science fiction short story I read in an anthology in a high school library sometime between 1962 and 1968.
In the 1920s and 1930s astronomers discovered that the giant planets - Jupiter, Saturn, Uranus, and Neptune, must not have solid surfaces that someone could stand on. Instead their atmospheres must gradually become thicker and thicker with depth until reaching stupendous density and pressure at the cores of the planets.
This knowledge took some time to be realized by a lot of science fiction writers and readers, and I have read a few stories in which the giant planets did have solid surfaces that lifeforms could walk on. Major science fiction writers published stories with solid surfaces on giant planets as recently as "Call Me Joe" by Poul Anderson, Astounding Science Fiction, April, 1957, and perhaps later.
The story I ask about seemed rather old fashioned in the 1960s.
In the story I ask about, Earth humans invade Jupiter, which has a solid surface. An Earthman defects to the Jovians, and aids them in their resistance to invasion (despite Jupiter in real life having 2.5 times the surface gravity of Earth, which shoud have incapacitated him).
Despite his help, the humans keep on winning, pushing the surviving Jovians farther and farther back, until there is only one small group of surviving Jovians left. As the Earthmen close in for the kill, the human protagonist explodes an atomic bomb or something, killing himself, the Jovians, and perhaps many of the attacking Earthmen.
So Edmund Hamilton's "A Conquest of Two Worlds" (1932), identified in John Rennie's answer, was in only one anthology early enough for me to read in that era, Every Boy's Book of Science Fiction (1951).
And here is a link to a list of the stories in it.