I HAVE SOLVED IT! Thanks so much for you believed in me, Bnus!
It took a long time and some money to solve my problem, but now it's fixed! I know there are many out there that have the same problem as me, so I give an explanation of how I did. Hope this helps you.
Try this:
Go to settings , system, storage and hard drive. then go the folder games and apps, find Halo 4 and go in there to remove everything related to Halo 4. I took away : Bullseye Pack ( downloaded items) War Games ( downloaded items) Spartan Ops Season 1.0 and 1.5 ( downloaded items) Halo 4 Title Update (update) Forge Island ( downloaded items) All, Halo 4 data ( saved games) Then go back to the HDD menu , and enter to Profiles . remove your profile. Go back to the HDD menu , and go to the System Items . remove everything that is there : Content Cache System ( Item ) The Marketplace - system data (system Item ) remove everything and everyone ! Now go back to Storage Devices, where you select the yellow Y button ( device options ) from the hard drive. not from your Cloud ! Now you need to Clear System Cache , 3 times in a row . THAT'S ALL ! Download your profile again and run Halo 4. And download everything it asks for when needed. Then last of all download your Bullseye -Pack or Champion Pack again , so it should work . It solved my problem anyway hope it does for you too.