Here is the full list of all 76 Robot Roller-Derby Disco Dodgeball achievements.
Perform three Top Gun KOs in a single life
Win 10 matches of FFA Deathmatch
Win 5 matches of FFA Elimination
Win 10 matches of Team Hoops
Get the winning score (any mode) after being KO'd
Achieve Rank 4 in your Mission Badge
Score 50 Combo KOs
Achieve Rank 3 in your Mission Badge
Get 250 Long Distance KOs
Achieve Rank 2 in your Mission Badge
Catch a ball thrown by an On Fire enemy
KO a player, then catch the ball they threw
Achieve Rank 1 in your Mission Badge
Catch an enemy ball that has been mid-air >= 4 seconds
Get the winning KO in Team Elimination 10 times
Be alive at the end of a Team Elimination match 25 times
Win 25 matches of Team Elimination
Be the Team Grand Prix Race winning player 10 times
Win 25 matches of Team Score Battle
Get the winning KO in Team Score Battle 10 times
Capture the enemy cube 100 times
Win 10 matches of Team Capture The Cube
Return your team's cube 25 times
Get 100 ninja hits
Win 5 matches of FFA Grand Prix
Get the winning score in Team Super Ball 10 times
Win 10 matches of Team Super Ball
Win 5 matches of FFA Hoops
Win 5 matches of FFA Super Ball
Win 10 matches of FFA Score Battle
Become On Fire with a Flying Squirrel KO
Win a match with a Helicopter KO
Perform a Godlike KO
Score one of every special KO type
Get 100 Multi-KOs
Win 10 matches of Team Grand Prix
KO the Grand Prix Race leader 25 times
Become On Fire while you are the Grand Prix race leader
Perform three Duck Hunt KOs in a single life
KO an On Fire enemy with a Long Distance shot
Get an 8 KO streak
Get a 5 KO streak
KO an enemy with a ball thrown 75 meters or more
Score 1000 points in Horde Mode (solo)
KO three enemies in 10 seconds
KO 100 opponents while On Fire
KO 25 opponents that are On Fire
KO an On Fire player while you are On Fire
KO an On Fire enemy with a Dunk
KO an On Fire enemy with a Helicopter
KO an On Fire enemy with a Flying Squirrel
Get 250 Dunk KOs
KO the Super Ball carrier 250 times
KO the Hoops Ball carrier 250 times
Score 5000 points in Horde Mode (solo)
Be the last team member alive in Elimination match vs 4+ live enemies and win
KO 1000 bots in Horde Mode
Get the winning KO in Team Deathmatch 10 times
Get the winning score in Team Hoops 10 times
Win a match with a Godlike KO
Catch 250 enemy dodgeballs
KO the Super Ball carrier with 3 or fewer seconds left, then win match
Catch a helicopter shot
Score the most hoops and most KOs in a round of Team Hoops
Get 10 Hoop Score Assists
Get 25 KO Assists
Catch what would have been the winning Deathmatch KO
Score 10 ricochet hoops
Win 25 matches of Team Deathmatch
Beat Arcade mode
Achieve Rank 5 in your Mission Badge
Achieve Rank 6 in your Mission Badge
Achieve Rank 7 in your Mission Badge
Achieve Rank 8 in your Mission Badge
Achieve Rank 9 in your Mission Badge
Achieve Rank 10 in your Mission Badge