To unlock the M1911 Handgun you must acquire 34,000 Pistol Score in Multiplayer. To check your progress on Pistol Score log into your Battlelog account (if you have one, if not simply make one it's free.) From the "Overview" screen click on the "Unlocks" tab and scroll down to the pistol section.
After getting the 34,000 Pistol Score your M1911 Handgun will be unlocked and will be able to be used as your sidearm for all classes in multiplayer. All you have you do now is get 45 kills with M1911 and you will unlock the achievement on the final kill required.