Just based on my experiences with crates & egg drops, I've only ever gotten them under luck reroll. (free from ally in the past and then from luck amulet).

The pattern I noticed with drops though is, outside of dungeons, I've only gotten something when there's 3-4 ppl on the map and their levels are very close to yours (or above you). I don't think the amount of damage you do to the boss have that much effect on your chance of getting them. People dying while attacking the boss does though. If somebody dies, you almost never get good drop.