This can be done during any group melee combat scenes. The first place where you will be able to do this is during the scene in the laundry room of the prison. There are other locations in which this can be done. To get a combo buddy takedown you will need to be in a fight where there are other people who are fighting with you. Sometimes the guy who is fighting with you will grab an enemy and you will finish him off, there are also moves in which you can double team an enemy. These are triggered automatically and occur fairly often. As long as you stay close to your allies, you should be able to get these to trigger for most enemies. The video below will give you a better explination on how to get this trophy.
Perform 10 combo buddy takedowns