Here is the full list of all 39 Muse Dash achievements. It takes around 20-25 hours to unlock all of the achievements on Windows.
Achieve grade "Silver S" of Heart-Pounding Flight on hard mode
Achieve grade "S" of Mujinku-Vacuum Track#ADD8E6 on hard or master mode
Hit the mascot character on the ENTER screen more than 10 times in a row
Get Full Combo in a stage
Clear a stage with only one "Great"
Select a song through Music Index, Difficulty Filter or Search and play it
Play a Lv.11 stage
Clear a song with Little Devil Marija
Clear a stage
Clear 20 stages
Clear 20 Hard Mode stages
Clear 10 Master Mode stages
Achieve grade "S" in a stage
Achieve grade "S" in a Lv.7 or Lv.7+ stage
Get Full Combo in 30 different stages
Totally knock back 100 BOSS's melee attacks
Totally knock back 300 Ghosts
Totally collect 300 Red Hearts
Totally collect 500 Notes
Totally knock back 100 enemies or BOSS's remote attacks while playing a Sheet (hold note)
Achieve grade "Silver S" in a Lv.7 or Lv.7+ stage
Reach 300 Combo in a stage
Totally unlock 14 characters
Totally collect 8 elfins
Totally collect 20 illustrations
Complete the tutorial stage
Clear a Mopemope stage at any difficulty level
Clear a Blackest Luxury Car stage at any difficulty level
Clear a Lights of Muse stage at any difficulty level
Clear a stage of I don’t care about Christmas though at any difficulty level
Clear an umpopoff stage at difficulty level "?"
Finish the tutorial April Fool's Day ver
Play any hidden sheet
Clear a Lv.4 or Lv.4+ stage without collecting Red Hearts
Clear a stage without knocking back enemies
Achieve only 1 "Miss" judgement in a Lv.7 or Lv.7+ stage
Achieve 100% accuracy in a Lv.6 or Lv.6+ stage
Get all achievements except hidden ones
Get all achievements