Instructions
Spinning Golden Cross
Select "Multiplayer" and then "Xbox Live" from the main menu.
Select "Callsign &Killstreaks" and then "Killstreak Rewards."
Put a check mark in the box next to the AC130 killstreak reward.
Find a multiplayer game and get 11 kills in a row (10 if you have the Hardline perk equipped) in order to use the AC130 killstreak rewards.
Shoot as many enemies as possible with your AC130. When finished, your character will have to die in order to obtain another AC130 or steal one from a care package.
Repeat Step 5 until you have 1,000 kills with the AC130 and completed the "Spectre IV" challenge. The spinning golden cross will unlock when the challenge is completed and progress of the challenge can be seen by navigating to "Multiplayer > Xbox Live > Barracks > Challenges > Prestige."
Spinning Green Star
Select Multiplayer and then Xbox Live from the main menu.
Select "Callsign &Killstreaks" and then "Killstreak Rewards."
Put a check mark in the box next to the Tactical Nuke killstreak reward.
Find a multiplayer game and get 25 kills in a row (24 if you have the Hardline perk equipped) in order to use the Tactical Nuke killstreak rewards.
Use the Tactical Nuke killstreak reward when your team is losing the multiplayer game to complete the "Ultimate Sacrifice" challenge. The spinning green star emblem is unlocked with the challenge.