Act 1
Bringing Fenris to the first meeting with the Arishok, and selecting the special companion dialogue option when prompted.
Selecting "I was promised future profits" at the first meeting with the Arishok, after he tells Javaris to leave.
Informing him of the deaths of his Qunari after the main quest Shepherding Wolves.
Act 2
During the main quest Offered and Lost:
Before attending Ser Varnell's rally near Darktown, informing the Arishok about his envoy being missing.
At the end of that quest, advising the Viscount not to burn the bodies.
After the quest, informing the Arishok about the deaths of his envoys (he responds respectfully whether you blame the zealots or not).
During the main quest Demands of the Qun:
If you did the mission To Catch a Thief, informing him about Isabela's involvement when meeting him alongside Aveline.
Agreeing with his principles during the dialog at the compound during Demands of the Qun - ratting out Isabela, saying the elves were right in their vigilante justice, and when he asks you what you would do, telling him you'd keep them rather than turn them over. (Do note this will annoy Aveline. If you take the ambiguous approach as to whether Aveline or the Arishok is right, the achievement will still unlock as long as you do the rest.)