Here is the full list of all 16 Dash & Swing achievements.
Die 10 Times in a Level
Play the game for the first time
Complete the first level
Try every radio station
Add a new song in the custom playlist
Unlock a new customizable
Complete all main levels
Beat World 1
Beat World 2
Beat World 3
Beat World 4
Destroy Something
Use a Portal
Invert Gravity
Get into Slooow Mooootiioonn
Go Into a Black Hole