You have to beat other people (especially those with higher stars than you) on the multiplayer games on the Main Street of every island. In the Main Street multi-player games, beat someone with more stars than you to advance your own rating. Other wins will also slowly build your battle rank.
Yes you can get 5 stars.
nothing
you have to go to the common room and click on a person and battle him. by battling the person you will earn stars. keep battling him to get 5 stars.
Beat someone with a higher star ranking than you
I guess you wait for another island.
Work hard.
This is the highest "Battle Ranking" for the multi-player games on Main Street. Beating additional players will not increase your rank past 5 stars.
What you have to do is play lots of games against other players. I started with one star and now, I have 5 stars! Play games against other people and you'll get it.
The "stars" are your "battle ranking" in the multi-player games on Main Street.
You try beating people with more stars in multiplayer games.
Once you reach 5 stars on the Battle Ranking in the multi-player games, there isn't any further advancement.
It means you were hit by something.