Here is the full list of all 32 Invector: Rhythm Galaxy achievements.
Hit 100 gates in Freefly.
Collect 1000 Perfects.
Land 15 Perfects in a row.
Get 25% Perfects on any song.
Get 50% Perfects on any song.
Complete a song on any difficulty in Single Player.
Hit all gates in a Freefly segment.
Complete a song on any difficulty in split screen.
Land 25 Perfects in a row.
Get 100% note completion on Normal.
Get 100% note completion on Hard.
Get 100% note completion on Ultra.
Boost without missing anything on Ultra difficulty.
Get 75% Perfects on any song.
Get an "A Rank" on 20 levels.
Get an "S Rank" on 20 levels.
Get an "S+ Rank" on 20 levels.
Get an "S+ Rank" on all levels.
Get a total score of 250 000 across all tracks and difficulties.
Complete all levels.
Get a total score of 1 000 000 across all tracks and difficulties.
Unlock all ships.
Complete the story by reaching the Origo Gateway.
Unlock all hidden songs.
Complete all challenge levels.
Twist the Tunnel 1000 times.
Jump 1000 times with the ship on the Road.
Complete 100 tracks.
Exit or restart from any ongoing track 100 times.
Unlock all worlds.
Visit the Sea of Dunes.
Collect 10000 Perfects.