When you begin, start going towards the mission marker, which will bring you to the courtyard. There will be a lot of enemies here, so begin clearing them out, including the second and third waves. Once everything is dead, go to the workshop door and you’ll be presented with two choices, to either lick through the candy cane barrier or go to the stables.
Note that if you choose the first option, it will take a good 5-7 minutes to get through the barrier (mash away) and you will still have to go to the stables. The upside is that you get the How Many Licks Does It Take? trophy/achievement. So, it’s entirely up to you if you want to do that, but afterwards, head to the stables.
There’s two stables and you will have to disable two reindeers at each one. Make sure you clear the area of enemies first so you don’t get interrupted. With that done, Twinkle will show up and you’ll have to chase him, leading to a group of "giant" elves. Defeat them all, as well as their leader, then get to the warehouse so you can get inside of the workshop.
Grab the disguise inside of the warehouse and then get to the present sorter. Once inside the workshop, clear it of the enemies, then go to Santa’s office, where you can pick up a "new" gun, which is really the Dubstep Gun with Christmas music. Use it to defeat Clawz (he’ll run away when his health gets low), then kill the rest of the enemies inside. Exit the workshop after that and get to the sleigh to finish the mission.