Updated: Halo 4 Campaign Weekly Challenge - 1/7/13

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The Challenges:
This Is Gonna Hurt - Complete any Campaign Mission on Heroic or higher difficulty with the Famine, Tilt and Thunderstorm skulls. - 2500 XP
So, you are likely going to see both of these challenges and think to do them at one time. However, due to the nature of Requiem, I would urge you to not do that. Requiem is a long and difficult level which will be made hard by the Famine skull as it is easier to run out of ammunition on Legendary difficulty. Now, the Famine Skull will cause all weapons on the ground to have half as much ammunition, the Tilt skull will modify the damage tables, and the Thunderstorm skull will upgrade all enemies. Instead, I would run through Dawn as it is the easiest level of the game and also has the most placed weapons so it will be unaffected by the Famine Skull.

Update: Apparently, this challenge actually wants you to have the Mythic skull on, not the Famine skull.  This means that completing "Requiem Rumble" will complete this challenge.  Thank you to everyone who pointed this out in the comments.

Requiem Rumble - Complete Requiem on Legendary difficulty with the Mythic, Tilt, Tough Luck and Thunderstorm skulls. - 6117 XP
Requiem, for me, was actually an immense pain to play through with a lot of Skulls on because the level is long and some of the level design is just mildly cruel to the player. The Mythic, Tilt, and Thunderstorm skulls together will make this even more painful as the Elites will be pretty brutal. This does not need to be done solo, however, so bring a friend. All of this level is just facing your standard Covenant forces so there are no special techniques except to make sure you utilize you armor abilities and just take it slow. Another thing to be mindful of is that you use appropriate weapons at appropriate times. I.e. do not waste a rocket on a single Grunt that you can just go melee. Conserving ammunition is very important for this level.

See the War Games Monthly Challenge here.
See the War Games Weekly Challenges here.
See the Spartan Ops Weekly Challenges here.
See the Waypoint Weekly Challenge here.