Spaceships or no spaceships? I'll assume no spaceships. Firing presents from railguns is awesome, but likely to result in presents of mass destruction
Okay, so a genetically engineered night-combat glide-capable artificially intelligent war construct... versus a Christmas-themed villain. OP says Santa is out of commission, but nothing about his sleigh, TARDISack, elves or stockpile of presents. As such, Christmas begins with Holly Sulfur ordering a bunch of elves to get their act together and prepare like normal (bar a small group of the strongest, fittest elves. She begins teaching this group basic hand-to-hand and melee combat techniques before finding the most weapon-like presents. Someone, somewher, will have asked for a metal window pole for Christmas, right?
One hour in, she tasks a pair of elves with flying the sleigh on a recon mission to locate nega-Santa. This will presumably take some time, but so will training the SPEC-ELFs and general organisation of presents. The sleigh is discovered to have been sabotaged, but Santa's factory has recently upgraded to 3D printers and so can create the required parts for repair. Five hours in, the sleigh leaves. By eight hours, the sleigh elves report contact with nega-Santa. They don't want to get too close and risk the sleigh. Holly orders them to return, and they do so. The SPEC-ELVES board the sleigh, and perform a combat drop near the town where nega-Santa hopes to make everyone sad. The fighting is bitter, and the SPEC-ELVES defeat nega-Santa's minions at great cost. Too few of them remain to defeat nega-SANTA, but he nonetheless retreats, unable to achieve his nefarious goals there. Holly orders the remaining SPEC-ELFs to remain and look after their wounded. No doubt they have enough wrapping paper for use as tourniquets and bandages.
Ten hours in, and the sleigh spots nega-Santa making his way to a smaller town. They lose track of him, but on closer inspection discover a hidden manhole. Using a My First Seismology kit, they discover a vast hidden underground base. Clearly nega-Santa has been preparing this for some time. When the sleigh returns, Holly decides she's had enough of this joker. Twelve hours in, she boards the sleigh, which heads back to the smaller town. After setting down, she gets the pilot elves to hide it in a copse of trees. Holly herself makes her way closer to the manhole, crawling the last kilometre. Her excellent night-vision notes movement, however. In the sparse trees nearby, she spots snipers. If they had infra-red, no doubt they'd have spotted her by now, but their behaviour suggested they didn't. Instead of going straight for the mahole, Holly decides to take out the snipers first. Crawling up to a tree then quietly climbing up it (her wing-claws giving an extra pair of grips), she reaches the first sniper. A lightning quick movement and the sniper is strangled into unconsciousness. For now, Holly tries to avoid escalating to killing - after all, so far Nega-Santa has only committed kidnapping and grand-theft Christmas. The SPEC-ELFs hadn't been able to give an account of losses before she'd left on this mission. She notes that the unconscious minion looks very much like an elf, but one from some child's nightmare.
Six trees cleared later, and Holly makes for the manhole. Once inside, it's much more difficult to see. Even her improved vision can't do much when there are no light sources. All there was, was a light in the long distance, which she headed towards. After rounding a bend, she was on a catwalk high over a huge space. At the bottom was unidentifiable machinery which hummed with power. A voice caught her attention. She couldn't make out the words, but there was Nega-Santa. He had a huge pointer, and was waving it at a massive projection on the wall. It was fairly obvious that it was Nega-Santa's plan for world domination from the words "WORLD DOMINATION PLAN" printed above several images. The images appeared to show a crying child and a crossed out present, then an arrow, followed by what sort of looked like the machine below. It was labelled "SADNESS AMPLIFIER". Another arrow, then a picture of the world leaders (with their faces photoshopped to look sad). Holly grimaced, trying not to make a louder reaction. Slowly, she edged backwards. He foot hit a small toolbox, which sent it clattering over the edge. She cursed, got up, and ran for the exit. Stealth was no use now, with tools falling from the catwalk onto the machinery of the sadness amplifier. Before leaving, she pulled a New Years day fireworks set, "Nuclear Demolition", from a black backpack and fired it down at the machine.
Back in the snow, she ran as fast as she could. Nega-Elfs sometimes blocked her path, but with no need for stealth, she just drew her sidearm and shot them. The weapon was self-cauterising, so if it hit nothing essential, it was unlikely to kill. Not that Holly imagined she hadn't killed people back in Nega-Santa's base, but by that point it was clear that Nega-Santa had to be stopped at any cost. She finally reached the sleigh, which took off as fast as possible. Suddenly, something whipped past, then again. One of the reindeer got hit, and it seemed that they were being fired on with tranquiliser darts.
"Behind you!" yelled one of the pilot elves, and Holly followed his look. Chasing them was a very angry Nega-Santa, with his own sleight. A missile separated from its underside. He seemed to be yelling something, but the wind took it. Holly turned back to the elves. "Make evasive maneuvers! You'll know when!" She took a few seconds to judge, then leaped from the sleigh. Her wings unfurled, and she glided right to Nega-Santa. He glared at her, and raised a huge lump of coal to throw. Holly saw a Swingball pole sticking out of a sack and grabbed it. She dodged the lump of coal, and noticed the pole had "Not for children under 3 years of age" written on it. She grinned, and brought it slamming down across Nega-Santa's chest. He screeched and fell backwards, off the sleigh. "Choke on it!" Holly yelled, before frowning because Nega-Santa wouldn't have heard it.
Using Nega-Santa's sleigh and sack, delivering the presents took half as long, so it didn't matter that they had wasted half the day not putting presents under trees.
The end.
