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