Supremacy is a big team mode with one match point to capture at the start then once captured you either go attack the other teams next area (if you cap the first) or defend your second area (if they cap first) There are 5 areas total, 2 for each team and one shared. This achievement wants you to get 10 kills whilst either attacking a control point or defending one, imo defending one is easier since the enemies come to you. You know when you're in a control point as there is a small area circled on your map when you are in it as well as the top of your screen will say 'Defending/Attacking'
This does not need to be done over one match and is instead cumulativeHere's an example of a control point on Hoth