Hey, it's my first time winning in Nightmare!  Yay!  :D  After trying a bunch of different challenge modes, I finally had a winning game in Angel of Doom.  :)
Scout with Gunrunner build seemed like the obvious choice, since it maximizes the dodge-convert-to-damage benefit of the challenge.  :)  I wore basic basic armour for the whole game, because I didn't want anything that would hurt my dodge chance (and therefore my damage bonus) too much.  I was pretty pleased with the combination of weapons I found;  my primary weapon was a 7.62 sidearm with enhanced damage and range, with occasional use of the rocket launcher if I wanted to kill things faster.  :P  And when I really wanted to clean up shop, the Jackhammer absolutely wrecked everything, when I had the ammo for it.  The auto-reload feature of Gunrunner took away that weapon's biggest drawback, and the AoD damage bonus let it shred even the largest enemies.  (Including the Summoner!)  :D  I also found that when I combined the damage bonus from using stealth with the AoD damage bonus, a rocket was able to gib Exalted Ravagers!  :o
I seem to have uncovered a couple of bugs in the mortem, though.  It says I cleared CalSec Central and Asterius Breach multiple times, presumably because after I cleared them, some enemies revived and I cleared them again.  (It even displayed the "Breach Vault Unlocked" message each time)  Also, it isn't showing the trait order, except the last skill I got, I'm guessing because it's trying to take up two lines, but only shows the second line?
Tormuse, level 18 Scout, defeated
The Summoner against all odds.
He survived for 10626 turns.
The run time was 4h 11m 40s.
He scored 9226 points.
He opposed the NIGHTMARE!
He was an Angel of Doom!
CALLISTO L3 -> Mimir Habitat L1
Mimir Habitat L2 -> CalSec Central
CalSec Central - cleared
CalSec Central - cleared
EUROPA L2 -> Asterius Habitat L1
Asterius Habitat L2 -> Asterius Breach
Asterius Breach - cleared
Asterius Breach - cleared
Asterius Breach - cleared
IO L2 -> Io Black Site L1
Io Black Site L1 - Secure Vault
Io Black Site L2 -> Black Site Vaults
BEYOND L2 - The Hunt
BEYOND L2 -> Limbo
Awards
  CRI Star (bronze cluster) (+25)
   * 25+ kills without taking damage
  CRI Star (silver cluster) (+50)
   * 50+ kills without taking damage
  Explorer Ribbon (+50)
   * Visited all encountered special levels
  Conqueror Ribbon (+100)
   * Completed all encountered special levels
  JoviSec Platinum Badge
   * Win any game on NIGHTMARE!
  Doomed Platinum Badge
   * Complete AoD on UV
  Doomed Diamond Badge
   * Complete AoD on Nightmare!
He killed 788 out of 885 enemies.
  32 archreavers
  25 fiends
  72 exalted ravagers
  15 plasma ravagers
  2 military bots
  53 exalted fiends
  11 rocket turrets
  40 turrets
  1 Summoner
  4 military sentrys
  22 security sentrys
  1 former CRI grunt
  12 CalSec bots
  69 exalted reavers
  1 former CRI soldier
  44 exalted kerbeross
  3 corrupted sergeants
  49 ravagers
  6 combat drones
  18 former soldiers
  5 former guards
  2 former heavys
  19 fire fiends
  16 siege ravagers
  3 former sergeants
  63 exalted soldiers
  12 cryobeross
  5 corrupted heavys
  9 CRI marines
  3 guardian bots
  6 hellish soldiers
  2 military drones
  4 corrupted soldiers
  4 former grunts
  7 toxic reavers
  26 ice fiends
  1 former CRI sergeant
  14 armored ravagers
  11 CRI bots
  10 reavers
  4 corrupted commandos
  5 cybeross
  10 security drones
  19 cryoreavers
  9 kerbeross
  14 former commandos
  24 CalSec sentrys
  7 toxibeross
  5 security bots
Traits
  Skilled L1
  Hellrunner L2
  Juggler
  Packrat L2
  Son of a Gun L2
  Gun hoarder
  Dash
  Eagle Eye
  Dodgemaster
  Second Wind
  Scavenger
  GUNRUNNER L3
Trait order
->
  Skl
Equipment
  Slot #1 : AV2 7.62 sidearm P
  Slot #2 : rocket launcher PA
  Slot #3 : 12ga jackhammer PA
  Body    : basic armor PB
  Head    : AV2 marine helmet
  Utility : AV2 pistol AMP
Inventory
  rocket (x10)
  rocket (x1)
  12ga shell (x44)
  7.62 ammo (x100)
  7.62 ammo (x100)
  7.62 ammo (x100)
  7.62 ammo (x78)
  plasma grenade (x2)
  gas grenade (x3)
  EMP grenade (x1)
  krak grenade (x3)
  smoke grenade (x3)
  CRI phase kit (x3)
  multitool (x2)
  large medkit