This quest is available in Trademond's Adventurers' guild after completing Festival Of Greed.
The first objective is just to talk to the white priestess about her request. The main objective is to slay the demon in the eastern forest of Runes.
You can access the eastern part of the forest from the central part. The entry point is blocked by a standard plant obstacle.
Once inside the eastern forest of Runes, you need to reach the demon's domain. The most obvious path is guarded by the Whiteoak. This enemy is probably far too strong at this point of the game to be defeated without using the Star Knightess power. There is also a path behind a standard enemy troop leading to a hidden hole. This constitutes a shortcut where using a rope and destroying a rock allow you to reach the demon without fightning the Whiteoak.
The boss you have to defeat is a low-demon accompanied by two insecurities. Here are some tips for the fight:
Once the demon is defeated, go to the guild to report and complete the quest.