The rule of characterization in fables goes like this: personality depends whole bunches on a character's type of being, specifically the type of animal. "Rikki-Tikki-Tavi" follows this rule to a T, and while we're here, does anyone know what that T stands for?
Rikki-tikki is a mongoose and acts as such. For example: "The motto of all the mongoose family is, 'Run and find out'; and Rikki-tikki was a true mongoose" (7). Notice how it doesn't say some mongoose families but all mongoose families. Since Rikki-tikki is a "true" mongoose, he will act like a mongoose in all respects, meaning he'll be doing a lot of running and finding out. In this tale, a mongoose is a mongoose is a mongoose.
The other animals get the same treatment. Darzee is a bird with a flighty disposition—get it? —and a love of song. Nag and Nagaina are snakes, so their cold-blooded physiology means they get cold-blooded personalities. Even Karait the common krait snake is cold-blooded by nature.
We might even say that this type of characterization is true for all Kipling's Jungle Books and not just "Rikki-tikki-tavi," but we'll leave you here with that thought. Feel free to read on and see if you agree with that statement.
Occasionally, the narrator just ups and characterizes a character. It doesn't happen often, but sometimes there's just no other way to get the characterizing done, son.
Take Rikki-tikki. When the narrator says Rikki-tikki was a "true mongoose," that's direct characterization at work (7). The narrator also tells us that "every well-brought-up mongoose always hopes to be a house-mongoose some day" (17) and that Rikki-tikki is inexperienced at fighting snakes (30). All these instances tell us exactly who Rikki-tikki is and explain his behavior in a direct a way as possible.
Other characters get the same direct treatment. The narrator mentions that Chuchundra is a "broken-hearted little beast" (39) and how Darzee is "feather-brained" while his wife is "a sensible bird" (78). Sometimes it helps just to be told what's what.
Food helps separate Rikki-tikki from his nemeses, Nag and Nagaina. (Just in case you didn't get it all the other times, the cobras are the bad guys.)
We first hear about Nag when Darzee mourns for the loss of his chick, whom Nag ate. Yep, Nag is a baby eater. On the other hand, Rikki-tikki mentions eating other animals twice: once when the humans feed him a piece of nondescript meat (13), and the other time when he considers eating Karait. So, in this story, it's not the fact that you eat other animals, but the type of animal you eat that aligns you as villain or hero.
But wait! Doesn't Rikki-tikki smash a whole bunch of baby cobra eggs? Yes, but the story makes it clear that Nagaina plans to infest the garden with her baby cobras, and this is a problem because each can "kill a man or a mongoose" (85). Plus he doesn't eat them simply to fill his belly. So Rikki-tikki's baby killing is totally different than Nag's. Right. Right?