During my play through of Dragon Age 2 I thought I was going to get the trophy/achievement for earning the Arishok’s respect, but as it turns out it is a bit tricky to get. Heads up if you’re not in act 2 yet (after the Deep Roads) then you may want to avoid this guide until you are done with that. Possible spoilers ahead!
You have to be honest and respectful with the Arishok always remember that.
At the start of act 2 in Dragon Age 2 you will get a quest called Black Powder Courtesy from the Viscount. Once that is completed he will ask you to talk with Seneschal Brann and he will give you a quest called Offered and Lost. Avoid doing it for the moment and go speak to the Arishok and tell him Your delegate is missing.
Alright now it is time to do Offered and Lost. After killing Ser Varnell you will have a talk with the Viscount. Tell him Do not hide it, he will know.
The last thing you have to do to earn the Arishok’s respect in Dragon Age 2 is during the quest Demands of the Qun. Once you get Demands of the Qun do not go to the docks right away. Instead make sure you have Fenris with you and you save. I have had this glitch on me once so be sure to save. Now head down to speak with the Arishok. Be as truthful as you can with him and you will earn the Arishok’s respect netting you the trophy/achievement A worthy Rival. Then you can continue with the story.
So there you have it the way to earn the Arishok’s respect in Dragon Age 2 as well as the trophy/achievement A worthy Rival. I hope it wasn’t to hard for you and you 100% the game.