Valid masks include:
Community - Happy Santa
Normal - Greedy the Elf, Rudelf, Krampus, Mechanical Santa, Mrs. Claus, and The Strinch
DLC - Furious Santa, Surprised Santa, and Tipsy Santa
Infamous - Mega Krampus
Valid outfits include:
Dapper Dashing Holiday, Dirty Santa, and Ho Ho Heister
The Criminal Carol 2022 colored Elf hats and Santa's Little Heister outfit were added after the achievement and it hasn't been updated to include them.
Tying or killing civilians doesn't affect it and the achievement can still be obtained on Breakin' Feds after the alarm has been sounded as long as you can finish before the point of no return.