Here is the full list of all 39 iO achievements.
Collect 50 medals
Play 50 levels
Complete level pack 2
Collect 25 medals
Play 25 levels
Complete level pack 1
Win 10 gold medals
Win 10 silver medals
Play 10 levels
Win 10 bronze medals
Shrink your ball 100 times
Complete all trial levels
Win a gold medal
Expand your ball 100 times
Unlock the full game
Play 75 levels
Play 100 levels
Play 125 levels
Play 150 levels
Complete level pack 3
Complete level pack 4
Complete level pack 5
Complete level pack 6
Collect 75 medals
Collect 100 medals
Collect 125 medals
Collect at least a Bronze medal in 150 levels
Collect at least a Silver medal in 150 levels
Collect at least a Gold medal in 150 levels
Expand your ball 1000 times
Expand your ball 10000 times
Shrink your ball 1000 times
Shrink your ball 10000 times
Collect a medal in all Impeccaball levels
Collect a medal in all Incrediball levels
Collect a medal in all Impossiball levels
Complete all Impeccaball levels
Complete all Incrediball levels
Complete all Impossiball levels