Escort the captain in force downstairs where he will teleport you into the Refectory Hall. The Captain lands next to the freezer so make your way there by killing the newly spawned mobs. Hail the Captain and cross the door to the freezer room for the quest to advance (i.e., for the escort portion to complete).
Loot the crystal from the nearest hanging meat. (If multiple people do this quest together it can happen that only one person can advance by moving around with the Captain, however if anyone in the group has just gotten the advance to get the crystal then you too can loot the crystal from the meat.)
Note: Do not exit the zone during this quest. It will more than likely bug, and you'll have to delete the quest and start over. Petitioning won't help - they know about the bug but will only reset the quest for you.