Unfortunately the ultimate anti-Cyberdemon build is currently bugged, in that Fireangel doesn't work. You can technically "dodge" all enemies, including Revenant's and Arch-Viles, but since their attacks target the tile next to you - and they always hit that tile - you get caught by splash damage anyways. With Fireangel, that doesn't touch you at all. Earning the
medal for wasting Cybie without damage
is childishly easy with a Fireangel shotty build.
Somehow intuiting the timing of enemy attacks is nigh impossible - even with a scout with a .65 move speed I still end up walking into facefulls of Sergeant buckshot every level - so the easiest way to handle Cybie is to dodge back and forth until he takes a shot. Then you know you've got a few rounds to whale on him until you see him reload his launcher. Then you dodge again till he blows his wad, and resume firing.
Chain-fire builds usually don't have a problem with Cybie, since chain-fire is all about tanking damage while dishing out
obscene amounts of pain in a very short time. They typically have a hyperblaster and some plasma for it as well, which helps cut through Cybie's obscene 4 points of armor, as well as putting incredible amounts of pain on in very short time.
But lets talk about your situation: killing Cybie with non-Fireangel shotty builds and pistol builds. Well, those are certainly harder.
First, pistols. Your first problem here (as I've found) is
reloading. Gun Kata is absolutely amazing for the free reloads, which is otherwise the fatal Achilles heel of the build. Against Cybie, however, it's utterly useless, which is how many successful Gun Kata AoMr runs have ended bitterly. Your second problem is
armor. Armor applies to each incoming projectile separately, so while it only takes the edge off explosions, it really puts the kibosh on rapid-fire attacks - and pistol-builds are rapid-fire. Think about it; you're effectively a manual chaingun. The third problem is ammo.
For reloading, you could face Cybie down with Speedloader Pistols - the mods for it aren't terribly hard to find (sometimes) and if you don't luck out and find some nice Unique pistols, and you don't get Whizkid before Cybie (more likely then not, both of them) you might end up facing Cybie with your early-game Speedloader pistols, and that isn't so bad, considering you'll really need the reload speed. And if you
do find Uniques, or make better weapons, it's a good reason to hold onto your Speedloader's for a bit.
Or you could bite the bullet (hurr) and take two ranks in Reloader. But as long as you're taking Reloader... consider passing up Gun Kata completely! Especially if you're having trouble with successful dodging and tend to corner-shoot anyways, you may as well go the full mile. Try a Technician pistol build - the single-pistol master trait concentrates massive firepower into fewer attacks, which will help greatly versus armor
and ammo conservation. (Especially if you save a 10mm ammochain for the Cybie fight; free reloads!) Or you could just go for Dualgunner, and dual-wield nasty Advanced assemblies pistols. Technician is
vital for this, because you get access to Whizkid immediately, instead of three traits in (two ranks of Finesse, then WK.) This is a simple inventory issue - by the time you get Whizkid with a Scout or Marine, you've been lugging around tons of precious mods, and leaving medpacks, ammo, phase devices, etc behind. With a Technician, you can pick up WK shortly before (or in) Hell's Armory and really clean house. (If you're not in the habit of killing the Shambler, do try if you're in decent shape. The two extra mod packs really help.)
Which brings me to my second suggestion: the
energy pistol. An advanced assembly, slightly superior to a normal pistol - but it uses power cells and does plasma damage. Plasma damage halves armor protection, very useful against Cybie, and even better, power cells are often more plentiful then 10mm deeper into Hell. And even with a 0.4 attack speed, the pistol doesn't devour cells the way Plasma Rifles like to. One will help, and if you're lucky enough to assemble two then you can just blaze through Cybie like he isn't there,
especially with two ranks of Reloader. Note also that the sweet pistol Uniques almost all have a looong reload time of 2.0 seconds, so Reloader is really important for using them well against bosses. Then there's the Blaster, which is basically a moddable plasma pistol that fires even faster and never, ever needs reloading. Pray to the deity of your choice for that one.
With a Technician dualgunner build you can still dodge by taking two ranks in Hellrunner (very useful for ducking behind corners to reload. Doesn't much help Reloader-less dualgunners because the typical 2.4 sec reload time usually ends with Barons strolling right up to your corner and whaling on you.) Or you can put those ranks into Ironman or Tough as Nails if you prefer.
Now, shotguns. Without Fireangel (allowing you to chip Cybie to death because he can't touch you) your options come down to Army of Darkness or rocket launcher as a secondary, since 8 effective armor vs. shotguns is bad juju. Now the nice thing about the Rocket Launcher; it fits most builds as a secondary weapon with just a mod or two. Launchers like Eagle Eye (for more reliable hits) and Reloader (one-shot and slow to reload.) Most builds will have at least one of those; for shotguns it's 2 ranks in Reloader. If you cleared out The Wall you should have the Missile Launcher, with perfect accuracy and a 5-rocket magazine; that should put some serious hurt on Cybie really quick. If not, slap an Agility Mod onto a Rocket Launcher (effective 10% in hits at max range) and go to town; with two ranks in Reloader you'll pump out rockets just fine. If you plan on lugging a few more stacks of Rockets then a Bulk mod - plus two ranks of Reloader - works miracles for the Rocket Launcher. The occasional miss isn't as devastating because you'll be pumping out rockets faster. The vanilla Rocket Launcher also keeps the Rocket Jump ability, which is very handy if you go with Army of Darkness.
MAD (Master Army of Darkness) makes shotguns
completely ignore armor; very powerful. However it also takes away Hellrunner
and Finesse, which is really, really harsh. You can't play active-shotgun worth a damn and your ability to dish out damage really fast is lacking, even with Piercing shotguns. Oh, no Advanced assemblies, either. Congrats, you're a corner-shooting hero. On the other hand, armor doesn't exist for you, so you can chip away at Cybie corner-shooting with a Combat Shotty like you're whacking imps on level 3. Unfortunately Cybie doesn't suffer knockback, so he'll be all over you very, very shortly. Now you've got two options, depending on location and situation:
1. Two to Tango. If he's really close, turn on Running and pray you can close to melee range before he blasts you halfway across the arena with a rocket. (If he does, see #2.) Then bust out the biggest, nastiest boomstick you've got, P-modded Double Shotty is preferable. Cybie's melee attack is nasty, but not as nasty as his rockets, especially since his rockets hurt just as much at 10 tiles as they do at 2, but your shotguns drop off fast with range - and when he rockets you, you get knocked back a ways. Then just step in diagonals around him to reload your shotty (or just reload stationary, if that's faster. Check by pressing @ to see stats.) 36 points of completely unmitigated damage each round will rip Cybie apart quick. Or...
2. DARING MUH-REEN ON THE FLY~ING TRAPEEZE~ Exploit the monstrous knockback of Cybie's rockets. This involves not tech-modding armor and taking off your boots if you don't desperately need any move bonus they might have. Also, put on the Phaseshift boots if you're lucky enough to find them. At least some of the time Cybie's attack will send you out of his sight radius... and if it doesn't, swap to your rocket launcher and rocket-jump even further away (your rocket's going to hurt a lot less then his, for sure.) Then just get out your Combat/Tac shotgun and spray buckshot in Cybie's general direction till he catches up to you, rinse, and repeat. (Note rocket-jumping away yourself is preferable to letting Cybie blast you.) With Piercing damage, your chipping will actually work.
And it
is chipping - Combat/Tac shotguns will hurt out to range 15 (your vision is only 8 tiles) but you can rack up some pretty impressive damage over time. Key phrase "over time." This is ammo-intensive. If Cybie catches you at close range you might want to take the oppertunity to get a much better kick in with your shotgun before he sends you a-sailing - or if you think you can swap to your rocket launcher before he nails you, let him eat your rocket as you rocket-jump away (enemies nearby take the brunt of that blast.) Be flexible. You could always keep your Tactical boots, tech-mod your armor and rely on two ranks of badass to just slog close to Cybie and kick him in the teeth with your double-shotty, if you think that'll work.
Just my... two dollars. And change. An hour successfully wasted, woop.