Here is the full list of all 17 Borealis achievements.
Get 10,000 points on arcade mode
Complete the neon mode without getting hit
Complete the rave mode without getting hit
Complete the symmetrical mode without getting hit
Get hit ten times in one minute
Complete the retro mode without getting hit
Complete the tile mode without getting hit
Go one minute without moving on survival mode
Complete the hyperspace mode without getting hit
Complete the digital mode without getting hit
Complete the summoning mode without getting hit
Get to level 1000 on survival mode
Complete the foggy mode without getting hit
Complete the underwater mode without getting hit
Complete the dogfight mode without getting hit
Complete the string mode without getting hit
Complete the celestial mode without getting hit