No, my drop rate sux balls as well...not just on this or other events but on basic adventures as well. There have been times it's taken me up to 3 months just to get 1/2 of what I need to get girls from the battles.
I'm confused on the shards, how do they work? Do I have to have the full amount to try to get the girl? I don't know what to do on obtaining the 6 star girls.