Buy or get keys to open the Luggages, you'll earn random parts of the collection, and When getting all 10 pieces will complete the collection, and unlock the achievement.
Luggage you have opened will occasionally give collection items at a relatively low drop rate. My suggestion is to continue working on a single location until you have completed the collection, even if later locations (and therefore more xp/$$ profitable locations) have opened. Don't move on to the next location until your collection is complete. It's a long grind to level 30 so this will give you a goal to focus on in the meantime.