Here is the full list of all 14 Spectraball achievements.
Clear every stage in order with no fallouts
Survive for 100 seconds in Crate Chaos
Survive for 60 seconds in Laser Jump
Survive for 100 seconds in the Arena
Complete the Space Construct Stage
Complete the Towering Mountain Stage
Complete the Sky Ruins Stage
Complete the Snowy Peaks Stage
Complete the Volcanic Crater Stage
Complete the Barren Desert Stage
Pull off 7 seconds of air time
Reach a speed of 100 mph
Complete the Tropical Isles Stage
Complete the Training Facility