Here is the full list of all 127 Pixel Galaxy achievements.
Collect a double-sword
Collect 1000 pixels
Destroy 1000 pixels
Have 10 Shield Pixels on your ship
Defeat The Chariot
Defeat Easier
Build a ship 10 pixels long
Build a perfect cross ship
Collect 500 pixels
Destroy 500 pixels
Restart 10 Times
Collect a divider
Die within ten seconds
Complete Tutorial 2
Die to a Bomb
Die within five seconds
Defeat Easiest
Defeat The Pixel
Destroy 100 pixels
Collect 100 pixels
Build a perfect 3x3 square ship
Collect a firestick
Complete Tutorial 1
Collect all achievements
Defeat Easy
Defeat Normal
Defeat Normaler
Defeat Normalest
Defeat Passive Easiest
Defeat Passive Easier
Defeat Passive Easy
Defeat Passive Normal
Defeat Passive Normaler
Defeat Passive Normalest
Get to 1000 secs on Easiest
Defeat the Galaxy on Easiest
Defeat The Blackhole
Defeat The Baron
Defeat The Disease
Defeat The Radiance
Defeat The Sonar
Defeat The Coward
Defeat The Rainbow
Defeat The Blade
Defeat The Nova
Defeat The Arcade
Defeat The Framework
Defeat The Serpent
Defeat The Storm
Defeat The Blossom
Defeat The Galaxy
Defeat all bosses
Defeat a boss in Colosseum Mode
Defeat half of the bosses in Colosseum Mode
Defeat all of the bosses in Colosseum Mode
Defeat the Pixel in record time in Colosseum Mode
Defeat the Blackhole in record time in Colosseum Mode
Defeat the Baron in record time in Colosseum Mode
Defeat the Disease in record time in Colosseum Mode
Defeat the Radiance in record time in Colosseum Mode
Defeat the Chariot in record time in Colosseum Mode
Defeat the Sonar in record time in Colosseum Mode
Defeat the Coward in record time in Colosseum Mode
Defeat the Rainbow in record time in Colosseum Mode
Defeat the Blade in record time in Colosseum Mode
Defeat the Nova in record time in Colosseum Mode
Defeat the Arcade in record time in Colosseum Mode
Defeat the Framework in record time in Colosseum Mode
Defeat the Serpent in record time in Colosseum
Defeat the Storm in record time in Colosseum
Defeat the Blossom in record time in Colosseum
Defeat the Galaxy in record time in Colosseum
Restart 100 Times
Restart 1000 Times
Destroy 2000 pixels
Destroy 5000 pixels
Destroy 10000 pixels
Destroy 50000 pixels
Destroy 100000 pixels
Collect 2000 pixels
Collect 5000 pixels
Collect 10000 pixels
Collect 20000 pixels
Collect 50000 pixels
Have 10 Speed Pixels on your ship
Have 20 Speed Pixels on your ship
Have 20 Shield Pixels on your ship
Build a ship 111 pixels big
Build a ship 150 pixels big
Build a ship 20 pixels long
Build a 7x1 ship
Die to a Bullet Barrier
Collect a bullet tunnel
Collect a laser
Collect a pincher
Rotate 50 Times in a game
Rotate 200 Times in a game
Time out a boss
Kill a boss in 5 seconds
Get to a boss with less than 10 pixels
Stay over 50 pixels large for 50 seconds
Build a ship to 100 pixels on Easiest
Build a ship to 80 pixels on Easier
Build a ship to 75 pixels on Easy
Build a ship to 60 pixels on Normal
Build a ship to 50 pixels on Normaler
Build a ship to 30 pixels on Normalest
Collect a large bullet weapon
Get to 400 seconds on Easier
Get to 400 seconds on Easy
Get to 200 seconds on Normal
Get to 200 seconds on Normaler
Get to 200 seconds on Normalest
Get a total score of 1000 seconds
Get a total score of 2000 seconds
Get a total score of 3000 seconds
Defeat The Mimic
Defeat the Mimic in record time in Colosseum
Defeat The Destruction
Get halfway through Boss Rush
Complete Boss Rush
Complete all Passive difficulties
Defeat the Destruction in record time in Colosseum
Defeat the Creation in record time in Colosseum
Defeat The Creation
Get a total score of 2500 seconds
Get a total score of 1500 seconds