Avatar wan sealed away vaatu with the help of raava.
Avatar Yangchen stopped the iron general from destroying the people he considered threats to his love.
Avatar Kuruk seeked revenge on Koh the Facestealer for taking away the face of his love.
Avatar Kyoshi stopped Shin the Conqueror and created the Kyoshi Islands.
Avatar Roku was there during the events that lead to the hundred year war and failed to stop firelord Sozen.
Avatar Aang finished what Avatar Roku had failed to do. He then broke the worldy illusion of the divided nations.
Avatar Korra stopped vaatu from returning and spreading dark spirits from engulfing the world. She then broke the illusion of separation between the spirit world and physical world.

I would love to see each of these events be explored more.