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