The narrator does a great job of telling us the protagonist's strengths early on:

Leiningen had always known how to grapple with life. Even here, in this Brazilian wilderness, his brain had triumphed over every difficulty...First he had vanquished primal forces by cunning and organization, then he had enlisted the resources of modern science.

These past successes have given Leiningen an unshakable self assurance that is rare in the average person.

We see the plantation owner prepare for the approaching ant colony with multiple levels of defense (from flooded ditches to petrol sprinklers to flaming motes) using man power and the technology available to him. Leiningen is also very skilled in handling his workers. Early on, simply his air of calm wisdom causes them to follow his lead, when their instincts would normally tell them to run. When the ants continue to encroach upon the house and outbuildings, so that the workers appear ready to abandon him, Leiningen cleverly uses reverse psychology to keep them there:

"Well, lads," he began, "we've lost the first round. But we'll smash the beggars yet, don't you worry. Anyone who thinks otherwise can draw his pay here and now and push off. There are rafts enough...and plenty of time still to reach them." Not a man stirred.

He knows none of them would dare lose face by quitting in front of the rest. And so Leiningen convinces his workers to continue risking their lives, even though none of them owns a penny of what they defend.

However, before we judge him for this, consider the ultimate strength with which he saves his ranch. When all else fails and the ranch is overcome with man-eating ants, Leiningen's stubborn perseverance will not let him lose. With nothing more than petrol-soak rags covering himself, he personally runs the considerable distance to the weir in order to open the river's flood gate, flooding his entire ranch and sweeping the ants away. At one point he is down, being eaten nearly to the bone, but he reasons that "He couldn't die like that! And something outside him seemed to drag him to his feet." True to his stubborn nature, he succeeds in saving the ranch and his workers, then recovers from near death to rebuild his property.

Leiningen, the titular protagonist of "Leiningen Versus the Ants," is a strong and wilful character. His most admirable strength is his insistence on fighting the ants with his men; while he could have instructed them to fight alone, and they would have agreed because of their respect for him, Leiningen is on the front lines with them at all times, directing and helping as they battle the ants. At the end of the story, as the ants seem poised to overwhelm the plantation, Leiningen decides to dam the river, an action of great risk:

"Now one of you might manage to get as far as the weir -- but he'd never come back. Well, I'm not going to let you try it; if I did I'd be worse than one of those ants. No, I called the tune, and now I'm going to pay the piper."
(Stephenson, "Leiningen Versus the Ants," classicshorts.com)

The ants have been shown to be a mob, moving and unthinking with no thought for their fellow ants. By taking the final blow into his own hands, Leiningen shows himself to be of a higher order than the ants, willing to sacrifice himself instead of ordering someone else to a possible death. Leiningen's self-reliance is an example of his individualism and refusal to place his life and importance over any other human.

In "Leiningen Versus the Ants", what qualities make Leiningen well equipped to fight the ants?

You asked two questions, so I have had to cut it down to one according to enotes regulations. I think Leiningen is clearly shown to have many excellent qualities in this short story that indicate he is more than able to combat the stampede of ants that is heading his way. However, interestingly, you might like to think about how some of these advantages might actually be considered disadvantages, given the arrogance that Leiningen begins the story with.

To me, the most important paragraph describing Leiningen as a character but also in terms of his qualities is as follows:

Moreover, during his three years as planter, Leiningen had met and defeated drought, flood, plague, and all other "acts of God" which had come against him - unlike his fellow settlers in the district, who had made little or no resistance. This unbroken success he attributed solely to the observance of his lifelong motto: The human brain needs only to become fully aware of its powers to conquer even the elements.

Leiningen, then, has a good history of experience with such "Acts of God", he is determined, and he is convinced of the power of the human brain to defeat "the elements." What is clear as the story begins is that he is also an inspiring, charismatic leader, who is able to call upon the loyalty of his men, which is another vital characteristic for the struggle he faces.