Shotgun damage drops off quite a lot with distance, and with Cybie's armour (and the fact that armour blocks twice as much damage from shells) it's quite possible to run out if you're keeping your distance. There's nothing better than dancing around him just outside melee range and unloading double shotgun into his face, but dodgemaster is a must for that kind of tactic.
Pseudoedit: I see you did have dodgemaster - you should have kept at minimum range throughout the fight. With dodgemaster, when you move, the first projectile of every monster will target the square you were standing on before you moved, so if you move around him, Cybie can't really hit you (except for spalsh damage if you are standing in front of a pillar). All you need to do is move until he shoot, and then you are free to shoot at him until you see the message (and hear the sound) that he reloads his rocket launcher. Until that happens, he can't hurt you (except in melee), so you are safe. Once he reloads, just move around some more until he wastes his shot. Repeat. With a bit of practice, you'll be able to take him down without taking any damage soon.
The other basic strategy for taking him down is going melee, getting berserk, and just cutting him up with a chainsaw. The Berserker trait is a must in that case though.