You need Popularity ranking (top row), Friendship ranking, Island ranking, Traveler ranking, and Splurge ranking. Popularity and Frienship can be opened using the compatibility tester, and Island and Traveler open once you get some visitors. For Splurge, you have to spend a lot of money on at least 1 Mii ($10,000, maybe?). I think that's cumulative, but I don't know for sure.