20 Reputation of the Mystras Residents can be earned by defeating the boss in purgatory for the first time in a week. This is reset on Monday at 04:00.
Additionally you get reputation as well as other rewards for completing the Purgatory instance by killing the boss depending on the difficulty.
10 reputation if the instance was opened by Key to the Cursed Holes.
25 reputation if the instance was opened by Key to the Perilous Caves.
45 reputation if the instance was opened by Key to the Corridors of Ashes.
Using a full crystal obtained from collections grants you with 25 Reputation as well as 5 Djinnar.