If you cannot obtain the Star Piece that Aoba carries after obtaining all of the other Star Pieces and Purple Coins in World 10-4, you will need to do the following:
Listen to Aoba's basic dialogue until she says she is busy helping everyone
Move out of her rescue room to any other section of the map, preferably 1-2 map rooms to the south.
Re-enter her room for the second part of her dialogue to play
You should now be able to obtain Aoba's star piece.