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