For completing the AA trial quest you receive a coffer with a piece of gear in it. This quest can be repeated several times a day but you can only receive the coffer once a week from the quest. The first 3 bosses drop blue pieces and the mage (last boss) drops purple set pieces. There is a set for each weapon/jewelry and gear light/medium/heavy. HRC has different blue sets that can drop but the last boss drops the same set pieces for the most part. The only thing that is different in the drops is the percent chances.