Medal of Honor Warfighter

When the sniper section starts, you will have to kill three guys. Do this, but wait until they're about to shoot, this makes it easier.

After the first three you will get two more targets. Kill one, it doesn't matter which, and
the other one will jump down and start shooting at the building you're in. After three shots, the building will collapse and you'll die. It's adviced to kill the second/fifth guy as soon as he's shot the first shot. From this point on he will remain stationary.

When you finally kill that guy, a friendly helicopter will come in the field and kill some enemies with Ak's. Then, you will be notified that there are two more targets on the hotel on the right. One is one the highest roof, and one is a little bit lower. If you don't kill them (fast enough), they will shoot down the helicopter and this will count as game over/dying. Now here's the fun part: You only have to kill the guy on the lower part because the helicpoter will kill the other one.
But stil, this guy is tricky. First, he spawns on the right part of the rooftop on which the other enemy is located, but he will walk around the back of the rooftop, to the left side. Once he is there, his first shot will destroy the helicopter, so you've got to be fast.

*EDIT 26-7*
You will complete the mission if you don't kill the last enemy, but this trophy won't unlock. So, sadly, you still have to shoot him.

Now here's something pretty important that if found out after 15 minutes of struggeling: when you shoot, you don't have to have the enemy in the middle of your crosshair. Instead, you also have to take distance into account. Luckily all targets have the exact distance between you and them 'written' above them.
Your crosshair shows numbers, with lines in between. These numbers represent the distance in 100 meters. For instance, a '2' means 200 meters. So if an enemy is 200 meters away, than you have to have the lower 2 on the enemy to kill him, rather than the center of your crosshair.

Hope this helps :)