In order to unlock this achievement, you have to have a total of 50,000 Brecilien Reputation. You can check your status by right clicking your avatar and select "Stats," then hovering over the Brecilien Reputation to see the total amount you have.
The quickest strategy to do this is to enter higher rarity wisps (Uncommon>Rare>Epic>Legendary). It's easier to find rarer Mists in common Mists than it is to run around and search for them in each map.
You can gain reputation by doing the following:
Rescuing Wisps
-This is recommended to have headphones, or sound at least, on. Use your mount to wander around the Mists and listen for a "distressed" wisp. Follow that sound and kill the mobs nearby to safely release it. Once you do, you gain reputation for it. This is considered the safest way to do this.
Enter Camps
-Once you enter a camp, an objective will pop up for you to kill monsters in the area worth a certain amount of fame in total. Once you reach that amount, you automatically gain reputation and have the ability to open a chest for rewards. Be warned, however, it is unrestricted PVP and being killed there will warp you back to your previous location. It's best to play it safe and leave the camps when someone is in there. Trust no one.
Escorting Wisps
-This is one of the riskiest ways of getting reputation. On the mini-map, a "Turbulent Mist" will pop up and will spawn a Weakeaned Wisp of Uncommon or higher rarity. Once you escort this wisp, a white portal on the mini-map will spawn in a random area that you can only see. Once you begin escorting the wisp, you will be marked for PVP regardless of your stance, meaning anyone can come kill you(where you warp back to your previous location), and take the wisp for themselves to bring. Doing this will also make you unable to use mounts, so gatherers use caution to be sure you're not overweight; and be sure to take advantage of your speed spells to get through as fast as possible. If successful, you can gain a lot of reputation for doing this.