Bravery sets Rikki-tikki apart from the other characters. Darzee isn't brave; he just cowers in his nest, hiding from Nag and Nagaina. Chuchundra isn't brave; he comes out at night to avoid danger. But Rikki-tikki, oh yeah, that guy is brave. He fearlessly jumps into a battle with Karait to save Teddy from certain death. He follows Nagaina into her cobra den to bring their battle to a permanent close. With the story presenting a type of moral lesson through talking animals à la an Aesop fable, one thing becomes clear: in the garden of life, definitely be the mongoose.
Rikki-tikki isn't a brave character. Since it's his nature to fight cobras, his fights are less about courage and more about natural instinct overriding all else.
Chuchundra knows about Nag and Nagaina's temperament. So, his helping Rikki-tikki is actually a brave act despite his overall cowardice.