Here is the full list of all 29 REPULSOR achievements.
Clear Arcade 10 times (any difficulty)
Reach LvL 45 in Infinite Octatron 2
Complete Arcade Hard
Complete Arcade without losing a single Life
Clear Arcade without letting the Core grow
Clear Arcade Hard without losing a Life and without letting the Core grow
Score 250.000.000 in Arcade Hard
Beat TRINITY - The Final Challenge
Reach LvL 50 in Infinite Octatron
Complete Arcade without Nova-Usage
Reach LvL 25 in Laserade
Score 30.000.000 points in Endless Mode
Achieve Level 15 in Endless Mode
Achieve Level 30 in Endless Mode
Unlock the Final Challenge
Complete Arcade Normal
Complete Arcade Easy
Score 250.000.000 in Arcade Normal
Reach LvL 35 in Infinite Octatron 3
Score 250.000.000 in Arcade Easy
Complete Stage 4
Achieve 9x Multiplier in any Mode
Complete Stage 3
Complete Stage 2
Complete Stage 1
Complete the Tutorial
Complete Arcade Mode in Coop
Ignite the Nova 200 times
Play REPULSOR at least 30 times