The time limit on this Bird of Prey skill feat seems very tight, and technically it is, but since you only need one run at the goal anyway, don't sweat it too much.
The gameplan is to sprint to the the tower with your marker, then jump off it and use Bird of Prey to execute 7 uruks. For the bonuses, you'll want to make sure that three of those executions are headshots, and that you're done in about 36 seconds.
Be aware that the tower you can see from the starting point is *not* your target- instead use your elven sprinting to run along the path to your true objective. It seems like running around the fences and obstacles here is slightly more time effective than jumping up and over them.
Leap to the top of the tower, then leap straight up and engage Bird of Prey. The time-slow feature here also slows the timer, so even a few seconds will be enough to complete the mission.
Just grant yourself the extra millisecond or so to ensure that your first few shots are headshots, and the rest is in the bag.