Before pursuing this, it is advisable to travel naked, because the only way you can safely get out after entering is using the Travel Planner, which teleporting costs depends on the inventory you have.
In order to enter Brecilien/Broceliande, you need to have 50,000 or more Brecilien reputation. Once you reach that amount, there is a chance that certain mists you enter will have a mirror-like white portal on the mini-map. Enter that portal to go to the city and have the achievement unlock. It doesn't matter the rarity of the wisp, so you can still enter the city through the common Mists.
Exiting the city will place you in a black zone. If someone kills you, you will lose all your inventory.