You don't need to kill every enemy you meet on your run. You will get the idea the more you run this game. For example, on 1.3 you can get past most of the level by killing only two enemies, which is the enemy on the bridge before the gates open and the warlord until you get to the last point and have to kill the enemies to trigger the cut scene. I was also confused at the start because I thought, they have an icon i must have to kill them but that's not the case. Unless the objective says to kill all of the enemies but if it says kill "insert name here" you just have to kill them