Here is the full list of all 12 R-COIL achievements.
Complete Level One
Complete Level Two
Complete Level Three
Complete Level Four
Complete Level Five
Complete Level Six
Die 100 Times
Shoot 1000 Enemies
Respawn in Stress Free Mode
Bring a friend back in Co-op Mode
Kill a friend in Duel Mode
Enter 'VITEKIM' in the High Score Table