After joining the Hunter’s Lodge in Meridian, talk to Aidaba to receive this quest. She’ll tell you that she’ll be giving you a special weapon for every fifteen Half-Sun, Full Sun, and Blazing Sun marks you show her. These marks are acquired for completing Hunting Ground trials. There are five hunting grounds in the game, each with three trials. The marks you’ll get depends on your performance in the trials, usually by completing the trials at the fastest time possible. If you get a Blazing Sun in a trial, you’ll also get the other “lesser marks” for that trial. That means getting a Blazing Sun in a trial will also give you the Half-Sun and Full Sun marks for that trial.
For more information about the individual hunting grounds, I suggest checking out the dedicated section for Hunting Grounds and how to get a Blazing Sun for each of them.
After securing a Blazing Sun for all trials, return to Aidaba to get your reward. You’ll obtain the Lodge War Bow, Lodge Ropecaster, and Lodge Blast Sling for bringing all marks. The quest will be complete as well but without any experience or resource bonuses.