so currently I am going around getting the adventurer achievements and treasure achievements
should I que for pvp or heroics to get the most ap?

I personally do heroics, which is super fast. But I am a tank and my friend is a healer so we just pull literally everything cause we're both over 840. If you have access to fast groups like this, then heroics is super good. Plus there's always the small chance of getting an 845 trink or a well-statted item, and the very small chance of getting a legendary.