Here is the full list of all 9 Papper Balls achievements.
BUY A BOMB BALL IN THE SHOP
BUY A MOON BALL IN THE SHOP
Hit more then 12 balls including 3 red balls in 1 hit
BUY A FOOTBALL BALL IN THE SHOP
BUY A AMERICAN FOOTBALL BALL IN THE SHOP
SHOOT DOWN 3 RED BALLS IN 1 HIT
Do not get into anything
SEARCH FOR THE BLACK HOLE
Hit more then 12 balls in 1 shot