Here is the full list of all 66 Spiralagon achievements.
Failed to complete a level one time
Failed to complete a level 10 times
Failed to complete a level 50 times
Completed a level one time
Completed a level 10 times
Completed a level 100 times
Completed a level 250 times
Completed a level 500 times
Completed a level 750 times
Completed a level 1000 times
All-time score of 50+
All-time score of 100+
All-time score of 150+
All-time score of 200+
All-time score of 250+
All-time score of 300+
All-time score of 350+
All-time score of 400+
All-time score of 450+
All-time score of 500+
All-time score of 600+
All-time score of 700+
All-time score of 800+
All-time score of 900+
All-time score of 1000+
All-time score of 1100+
All-time score of 1200+
All-time score of 1500+
All-time score of 1700+
All-time score of 2000+
All-time score of 2500+
All-time score of 2700+
All-time score of 3000+
All-time score of 3500+
All-time score of 3700+
All-time score of 3900+
All-time score of 4000+
Completed a Level in Speed mode
Completed a Level in Greed mode
Completed a Level in SpeedGreed mode
Completed a Zone in Speed mode
Completed a Zone in Greed mode
Completed a Zone in SpeedGreed mode
Completed a Campaign in Speed mode
Completed a Campaign in Greed mode
Completed a Campaign in SpeedGreed mode
Failed to complete a level 30 times
Used SpeedBoosts 10 times
Used SpeedBoosts 50 times
Used SpeedBoosts 100 times
Used SpeedBoosts 500 times
Used SpeedBoosts 1000 times
Used JumpBoosts 10 times
Used JumpBoosts 50 times
Used JumpBoosts 100 times
Used JumpBoosts 500 times
Used JumpBoosts 1000 times
All-time score of 5000+
All-time score of 6000+
All-time score of 7000+
All-time score of 8000+
All-time score of 9000+
All-time score of 9999+
Success in the final second
Success in the final three seconds
Success in the final ten seconds