Here is the full list of all 31 Symphony achievements. It takes around 20-25 hours to unlock all of the achievements on Windows.
Play 840 minutes
St Matthew Passion, BWV 244
"A note of shortened duration separated from the note that may follow by silence" - Find and equip the rare Sonic weapon
"A title of extreme respect given to a master musician" - Reach the 4-gold star rating on 10 songs
"Bang the piano with the fist" - Get 100% completion and over 30,000 points at the Fortissimo difficulty
"Always" - Reach 30,000 points and finish without dying at the Fortissimo difficulty
"Performing with exceptional ability, technique, or artistry" - Perfect game (100% + no death) and over 30,000 points at the Fortissimo difficulty
Symphony No. 104 in D major (Hob.I:104)
"Warlike, bellicose, belligerent or combative" - Get 100% completion and over 30,000 points at the Mezzo-forte difficulty
"With fire / in a fiery manner" - Perfect game (100% + no death) and over 30,000 points at the Mezzo-forte difficulty
"With spirit / vigor" - Get 100% completion and over 30,000 points at the Piano difficulty
"Ignited / on fire" - Perfect game (100% + no death) and over 30,000 points at the Piano difficulty
"Silent; do not play" - Get 0% completion
"work" or "labour"; a number generally assigned by composers to an individual composition or set of compositions on publication, to help identify their works - Finish the game
"A gradual increase in volume of a musical passage" - Find and equip the rare Charging weapon
Unlock Fortissimo difficulty
Symphony No. 5 in C minor, Op. 67 (hint: 67 is the key)
Unlock Forte difficulty
Upgrade a weapon to level 5
"Leads a musical ensemble by way of visible gestures" - Reach the 4-Silver star rating on 10 songs
"Obstinate, persistent; a short musical pattern that is repeated throughout an entire composition" - Reach 30,000 points and finish without dying at the Mezzo-forte difficulty
Unlock Mezzo-forte difficulty
"Leader of the first violin section" - Reach the 4-bronze star rating on 10 songs
Unlock Mezzo-piano difficulty
"A large instrumental ensemble that contains sections of string, brass, woodwind, and percussion instruments" - Equip 4 different weapons simultaneously
"Sustained, lengthened" - Reach 30,000 points and finish without dying at the Piano difficulty
Defeat the first boss
Equip a new weapon
Reach a score target
"A group of people who perform instrumental or vocal music" - Perform a 10X chain
"A group containing five members" - Perform a 5X chain