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