First off, Rikki-tikki’s Brave he went into the hole with Nagina when it was very risky. Rikki-Tikki risked his life for the humans by battling Nag and Nagina. He is brave by confronting Chuchundra.He was Brave to help darzee and his wife by dealing with nag.
In addition, Rikki-tikki is protective, he wanted the sleep on teddys chin so he could protect him from Nag/Nagina. He's protective because he risked his own life