Here is the full list of all 31 Impossiball achievements.
Play a game of Loneball with the Power ups off, music volume set to zero, a score target of 11 and the classic camera angle
Return 100% of any serve
Reach a total of 10,000 points
Reach a total of 50,000 points
Reach a total of 100,000 points
Return and score a point with Invisiball active whilst playing Loneball
See every serve at least once
Beat the CPU at Singles Impossiball on Easy 10 times
Beat the CPU at Singles Impossiball on Medium 5 times
Beat the CPU at Singles Impossiball on Hard once
Beat the CPU at Singles Loneball on Easy 10 times
Beat the CPU at Singles Loneball on Medium 5 times
Beat the CPU at Singles Loneball on Hard once
Beat the CPU at Singles Dodgeball on Easy 10 times
Beat the CPU at Singles Dodgeball on Medium 5 times
Beat the CPU at Singles Dodgebll on Hard once
Complete a full match in any game mode on every camera angle
Avoid getting hit by a ball in Dodgeball for 20 seconds
Win a maximum value point on Dodgeball
Win a maximun value point on Impossiball
Win a match of Impossiball or Dodgeball with a maximum value point whilst behind on points
Win a game of Impossiball with 'Own Goals' turned on
Beat the CPU at Doubles Impossiball on Easy 10 times
Beat the CPU at Doubles Impossiball on Medium 5 times
Beat the CPU at Doubles Impossiball on Hard once
Beat the CPU at Doubles Loneball on Easy 10 times
Beat the CPU at Doubles Loneball on Medium 5 times
Beat the CPU at Doubles Loneball on Hard once
Beat the CPU at Doubles Dodgeball on Easy 10 times
Beat the CPU at Doubles Dodgeball on Medium 5 times
Beat the CPU at Doubles Dodgeball on Hard once