I don't entirely agree with LuckyDee. Speaking as someone who has never been able to 100% avoid getting hit, TaN and Ironman are very helpful in preventing late game instadeaths. Certainly, the ideal would be to avoid damage completely, but if you look at my mortems, you may notice that I rarely go a whole game without TaN or Ironman. In fact, if I have the opportunity, such as in Ao100, I'll max out both traits. (I would max them out in my early games too; for a long time when I was a seasoned beginner, it was the only way I could win)
As for this situation, yeah, it sucks when the RNG throws you into a situation like this, facing a group of Arachnotrons with no cover. :| Sometimes, avoiding damage is impossible and you just have to try to limit it. For example, perhaps, in this situation, you could have run up to the Arachnotrons in the first few seconds before they woke up, and shot them at point-blank range while they could only hit you with their melee attack which does considerably less damage than their plasma barrage. Or perhaps you could have gone into the lower-right corner of the room, out of view of most of them so that fewer of them could shoot you at a time? It's hard to tell from the screenshot if any of those options are viable; just a couple of ideas off the top of my head.
EDIT: Also, I like your changes to the mortem. "Resistance is futile!" Heehee! :)