What are the episode names to Avatar book 3 chapter 13 - 21?

You're asking for the episode titles of Avatar: The Last Airbender Book 3: Fire Lord's, Chapters 13-21. Here they are:

Chapter 13: The Ember Island Players

Chapter 14: The Day of Black Sun, Part 1: The Invasion

Chapter 15: The Day of Black Sun, Part 2: The Eclipse

Chapter 16: Sozin's Comet, Part 1: The Phoenix King

Chapter 17: Sozin's Comet, Part 2: The Old Masters

Chapter 18: Sozin's Comet, Part 3: The Avatar and the Fire Lord

Chapter 19: The Western Air Temple

Chapter 20: The Firebending Masters

Chapter 21: Avatar Aang