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