You have to bomb the entire enemy team with a single airstrike.
It could be a stealth bomber, which is easier.
kill somebody just before he/she earns an 10 or more killstreak
Complete the Flawless challenge Survive the entire game see related link
You have to complete the Pavelow III challenge, which I believe is call in 25 Pavelows.
In order to complete the cluster bomb challenge, you have to kill 5 enemies with a single air strike. I suggest using the stealth bomber with UAV for this. A recommended game type would be ground war.
You have to get invited by a co-host or a host that hosts challenge lobbies
complete challenge "silent veteran II"
complete challenges from the barracks , gennerally the harder the challenge the cooler the title
Complete the "Omnicide!" challenge which is killing the entire enemy team in 10 seconds.
kill somebody just before he/she earns an 10 or more killstreak
Get 50 kills with an AC130. You must be prestiged in order to complete this challenge.
unlock at rank 41 after completing "Rival" challenge.
You do not challenge Infinity Ward
You have to complete the 'Rival' Challenge where you kill the same player 5 times in a single match.
Complete the Flawless challenge Survive the entire game see related link
You have to complete the Pavelow III challenge, which I believe is call in 25 Pavelows.
Complete the Challenge "Ultimate Sacrifice". Call in a nuke while your team is losing.
Get into a challenge lobby.