Here is the full list of all 68 Runbow achievements.
Play 1000 multiplayer rounds
Play 500 multiplayer rounds
3 medal all of Out of This World
Defeat Plunto
Beat all of Out of This World
Play 300 multiplayer rounds
Play a lot
Die 100 times in the Bowhemoth
Go through 20 portals
Beat the Bowhemoth
Beat the Bowhemoth in 60 deaths or 60 minutes
Play 100 multiplayer rounds
Unlock all gallery content
Beat all levels in Adventure mode
3 medal all levels in Adventure mode
Beat adventure mode and defeat Satura
3 medal all levels in the Nightmare map
Beat the boss in the Nightmare map
Beat all levels in the Nightmare map
Unlock every guest character
Play a level in each Adventure map
3 medal all levels in the Island map
Beat all levels in the Island map
Play 10 multiplayer games
Do 20 taunts in one game and win
Beat 10 Adventure levels with a friend
Land the most hits & get the least wins in a game
Get the Lightning power-up 10 times
Get the Mimicry power-up 10 times
30 seconds in push zones
Get the Swapper power-up 10 times
Win when an enemy has 1 second or less
Play King of the Hill
Play 7 multiplayer games
30 seconds in pull zones
Get the "Everyone Gets a Title" title
Land 5 Super Punches
Play with 9 unique costumes/characters
Be stunned when you get the trophy
Land one of each type of attack
Do 10 Butt Pounds
Play a game without anyone else scoring
Play 5 multiplayer games
Play Arena
Land 20 hits in one game and win
Win a tie-breaker
Play 2 multiplayer games
Play a Run game
Taunt 20 times
3 medal all levels in the Forest map
Beat all levels in the Forest map
Beat the boss in the Forest map
3 medal all levels in the Prison map
Beat all levels in the Prison map
Beat the boss in the Island map
Run a total of 42,195 meters
Set the Fun type to Maximum
Set the Fun type to Kawaii
Get 3 medals in 15 Adventure levels
Beat 100 enemies
Beat the boss in the Prison map
Fall to your death 20 times
Get 3 medals in 10 Adventure levels
Break 30 breakable blocks
Jump upwards 1609 meters
Spend more than 3 minutes in the air
Get killed by a laser
Beat the Bowhemoth in 10 deaths or 20 minutes