You may have heard that phrase when someone is extremely confident that they are going to get someone else to do something. Where did it come from?
I actually found the answer from a Word Reference message board. I know forums aren't super reliable for factual information, but this one (from firefoxbrand) seems legit.
It's a phrase used by the Navy's military police, the Shore Patrol. It's the Shore Patrol's job to control the behavior and crimes of the Naval personnel when the Fleet is in town.
When a sailor causes trouble of some kind (like gets in a fist fight, for example), sometimes the Shore Patrol will deal with it quietly. However, in cases where the sailor doesn't stop their defiance, the Shore Patrol will write up the infraction and it will go on the sailor's permanent record. This is a much bigger deal, as the sailor could be discharged as a result.
So, as I understand it, "kicking ass and taking names" means that the Shore Patrol not only "took care of" the crime, but "wrote up" the offense, too.