Try investing a point into hellrunner. You'll probably want to have dodgemaster before cybie.
I've recently put quite some time into research of how to pass the anomaly on AoHu (10 HP max, so you really don't want to take a scratch)
here.
You can see the time it takes you to move on the character information screen (@). Note that the number changes when you enter running mode.
I know for a fact that you can pass the first room in the anomaly if you have (while running) speed 0,38 without taking a single hit. That may be hard to achieve in builds not made for running, but I believe that if you are a tad slower, you should survive the experience.
BTW, you must go towards the door you came from. The other one is closer, but you have to open the door, plus the lost souls spawn closer to it, not to mention the cacodemons.
In any case, there is often a phase device you can use instead, I believe I found it in about half of my games.