No you don't have to get every card, chest, and chocograph, but you can't miss much. You need to open as many chests as possible, as well as collecting cards and playing Chocobo Hot and Cold. I believe the more you steal the higher your rank goes as well.

For attaining "S Rank" (the highest rank), Alleyway Jack reveals his true identity (SPOILER)Gilgamesh and hands over the "S Rank Badge" (or something like that) which is your prize from the Treasure Hunting Guild.

So all in all, it's basicall pointless.