What characteristics most help Rikki-Tikki defeat the snakes?

The basic characteristics that Rikki-tikki has that allow him to defeat snakes are the basic characteristics of a mongoose. A mongoose is a natural predator to snakes of all kinds; therefore, Rikki-tikki has been blessed with innate abilities that work in his favor. One such characteristic is his quickness. Being as fast or faster than the strike of a cobra or an Eastern brown snake is fast.  

The victory is only a matter of quickness of eye and quickness of foot—snake's blow against mongoose's jump—and as no eye can follow the motion of a snake's head when it strikes, this makes things much more wonderful than any magic herb.

Readers get a clue early on as to how quickly Rikki-tikki can move. Nagaina tries to catch Rikki-tikki by surprise from behind, and he is able to quickly jump out of the way of the strike. A few paragraphs later, Rikki-tikki defeats Karait. Readers are specifically told Karait is exceptionally quick because of his size.

If Rikki-tikki had only known, he was doing a much more dangerous thing than fighting Nag, for Karait is so small, and can turn so quickly, that unless Rikki bit him close to the back of the head, he would get the return stroke in his eye or his lip.

Another characteristic of Rikki-tikki that allows him to defeat the snakes is that he is smart. He knows when to press his advantage and when to back off.  

Rikki-tikki did not care to follow them, for he did not feel sure that he could manage two snakes at once.

Finally, Rikki-tikki is brave. Taking on dangerous snakes is brave to begin with; however, the story ends with Rikki-tikki following Nagaina into her home territory. This act is something Rikki-tikki knows is especially dangerous, but he knows he must kill her for the safety of everybody.  

And very few mongooses, however wise and old they may be, care to follow a cobra into its hole. It was dark in the hole; and Rikki-tikki never knew when it might open out and give Nagaina room to turn and strike at him.