Wow, last month of the year. Start eating your advent calender chocolates guys.
Blastin' and Relaxin' - Kill 180 enemies in any game mode in Reach - 2343cR
Any game mode and you've got a lot of Firefight to work through today, about 2-3 games worth depending on luck and skill. Firefight's often the fastest way for this anyway.
Demon - Kill 50 Elites in Firefight Matchmaking - 3000cR
Now, I'd suggest either solo in Scoreattack x2 (The last round is very Elite Heavy) of Some ArcadeFight in the Firefight Doubles playlist (Preferably with a friend). The Heretic waves are filled with Elites.
The T.G. Opposition - Kill 100 enemies in Firefight Matchmaking with the Shotgun - 3000cR
Sticking with the Scoreattack x2, the weapon set you want is the Pistol/Shotgun. This is a good set as the pistol gives headshots and the shotgun gives, well, shotgun kills. So you can get this challenge and the next one easily at the same time) Choose when to use what gun (Shotgun for wave 1, 3 & 5, Pistol 2, 3 & 4)
Hyper Lethal Vector - Kill 100 enemies with headshots in Firefight Matchmaking - 3000cR
Now, Arcadefight gives you the Shotgun/Grenade Launcher and Sniper/DMR sets. Both useful for these challenges. As rounds can mix up, it's up to you to select what weapons for what round. Maybe start with the shotgun though, once some of those skulls go on, you don't really want to stay too close to the action.