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There is an invading force in the shape of a crescent. Supersmart aliens gather as many aliens from the galaxy as they can. The main character is told he needs to form bonds with the humans to make him a better fighter. Then he is put on a space ship with other aliens. The human fights all and wins except for the heavy worlder. The heavy worlder gives in. So they train and train and when the battle comes everyone else starts to flee but the human led ship.

Hour of the Horde, a 1970 novel by Gordon R. Dickson, also the answer to this old question and an unaccepted answer to this one. Does any of these covers ring a bell? A version (probably shorter) was published in Venture Science Fiction Magazine, May 1969, which is available at the Internet Archive. If I have a copy of the book I don't know where it is, so the quotations below are from the magazine version.

There is an invading force

". . . These gentlemen," went on the presidential voice slowly, "have explained to the representatives of the nations of our world that our galaxy of millions upon millions of stars, of which our sun is a minor star, out near the edge—" The figures of the two men disappeared and were replaced by what looked like a glowing spiral of dust floating against a black background, "will shortly be facing attack by a roving, intergalactic race which periodically preys upon those island universes like our galaxy which dot that intergalactic space.

in the shape of a crescent.

Meanwhile, computer-created before them all now, there had appeared on the vision screen before them something like the shape of a silver crescent—in the light of the artificial sun over the battle line. A silver crescent, horns forward, pointing toward them. It was, Miles' Center Alien-implanted knowledge told him, a reconstructed image of what the Silver Horde had looked like, attacking this galaxy a million years before.

Supersmart aliens gather as many aliens from the galaxy as they can.

"Their civilization, which represents many worlds in many solar systems in toward the center of the galaxy, has taken the lead in forming a defensive military force which will attempt to meet these predators at the edge of our galaxy, and turn them aside from their purpose. They inform us, that if the predators are not turned aside, over ninety percent of the life on the inhabited worlds of our galaxy will be captured and literally processed for food to feed this nomadic and rapacious civilization. Indeed, it is the constant need to search for sustenance for their overwhelming numbers, that keeps them always on the move between and through the galaxies, generations succeeding generation in rapacious conquest."

The main character is told he needs to form bonds with the humans to make him a better fighter.

"Our visitors have told us," he said, "that defense of the galaxy is a common responsibility. For our world to join in that defense, is therefore a duty. What they require from us, however, is a contribution of a highly specialized nature." His voice hesitated, and then went on, more strongly. "They tell us that the weapons with which our galaxy's defensive force will meet the Horde are beyond the understanding of our science, here on Earth. They tell us, however, that they are part physical, part non-physical in nature. The number of fighting individuals we can contribute to our galaxy's defense is therefore limited by our relatively primitive state of awareness as far as these non-physical forces are concerned. We can send one man, only. This one individual—this one man, who is best suited to be our representative by natural talent and abilities—has already been selected by our visitors. He will be shortly taken over by them, adjusted so as to make the best possible use of these talents, and then turned loose for a brief period to move about our world and absorb an identification with the rest of us. This process of absorbing an identification has been compared by our visitors to the process of charging a car battery, to exposing its plates to a steady input of electrical current. Once he has been so 'charged', all of us on this world who have managed to contribute to the 'charging' will continue to have some sort of awareness in the back of our minds of what he is going through up on a battle line to which he will be transported. And from this linkage, he will draw the personal non-physical strength with which he will operate his particular weapon when the encounter with the Horde occurs."

Then he is put on a space ship with other aliens.

"This ship," said the taller alien, quietly, "is the smallest of our scout ships. It is staffed by twenty-two individuals, each a representative of a world like your own. You will become the twenty-third, and last individual to make up its crew. In the weeks to come, you, with the others, will learn to maneuver it and together use its single weapon. Now, follow me. I'll take you to join the rest of the crew."

The human fights all and wins

Thee was evidently a pecking order aboard, a social system in which each member of the crew was deferential to those above him and contemptuous of those beneath. There were no equals on the ship, then. Obviously, the way you moved up in rank was to fight your way up, as he had fought and beaten Chak'ha, thereby making Chak'ha last and least.

So, now with his victory over Chak'ha, he was second from the bottom in that order, thought Miles. Why—the remembered, inviting white passion of battle glowed suddenly again to life inside him—all he needed to do to improve his situation on this ship, was to fight his way up through the ranks. There could be no danger of losing his life in the process, since evidently the Center Aliens who had built the vessel, had made provision against such killing.

except for the heavy worlder.

"—I tell you," Miles kept insisting to him stubbornly, "that Luhon has to have a weak spot! Any organism, by its very nature, has to have drawbacks as well as advantages."

"To be sure he has to have weak spots," replied Eff, shrewdly. "But are they weak spots that you have strong spots to correspond with? Luhon's simply too fast for you. He's too fast for any of us aboard here. He's from a heavy world—one where the gravity is much more than any of us are used to."

The heavy worlder gives in.

It was just beginning to sink into him now that Luhon had actually given way, had stepped down and allowed him, Miles, to take top position aboard the Fighting Rowboat.

So they train and train

"Practice," answered Miles, harshly. "That's what we can do. Practice using the weapons without getting worked up about it.—I know it won't be easy to do," he went on as Luhon opened his mouth to speak again, "but we can try—and maybe we can break through what's blocking us, this way. We'll start right now. We're all dead tired. It should make it that much easier to damp out our emotional reactions."

and when the battle comes everyone else starts to flee

It was true. After everything—after all their work and the work of the Center Aliens and others to set up this Battle Line—now just because of some cold answer given by an unliving device, the greatest strength the galaxy could gather was not going to face the Horde after all. They were all going to turn tail and run, save themselves, and let the Horde in to feed upon the helpless worlds they had been sent out here to protect.

but the human led ship.

Miles hands slapped down on the console in front of him. To his right, Luhon's flashing gray fingers were already blurring over his controls, and Eff was busy at his left.

Like a living creature with one mind, the Fighting Rowboat lifted from its cradle and flashed into shift—single-handedly and alone against the uncountable numbers of the Silver Horde.