Unlike the Superhero Collection, you can get more than one piece per day via Mystery Bag. The most I've picked up in 1 day has been 3, but sometimes you won't get any. Just keep plugging away at it and talk to your mafia if you get extras and attempt to swap some out.
Great reward for vaulting this collection as you get 20 skills points to allocate as you please. Doesn't seem to be any that are more difficult to get than the others, just give it time and open as many Mystery Bags as you can.