Here is the full list of all 27 MUSYNX achievements.
Get 18000 EXACT note marks total
Play 10 different songs in a row
Get a total of 5000 EXACT note judgements
Play a total of 10000 notes
Get one EX rank
Select Exit when you play a Lv.10 or above song
Get 118% Syncrat on any song
Complete HD mode once
Get EX rank on 3 songs
Get 120% Sync on any song
Get EX rank on 10 songs
Collect All Available Trophies.
Get one B rank
Play one song 8 times continuously
Speak to the shopkeeper 10 times
Get a total of 30 EX ranks
Play a total of 50000 notes
All Songs Average Sync to 110%
Complete any song at 6 different stages
Play one song 15 times continuously
Get one EX rank at 6K Mode
Get a total of 100 EX ranks
Any Song get 122% Sync
Get 50000 EXACT note marks total
Play a total of 200000 notes
All Songs Average Sync to 115%
Play All Songs, All Difficulties, and All Modes