To unlock the Best of the Best trophy in Call of Duty: Modern Warfare Remastered, you will need to complete the cargo ship mockup on the F.N.G level in under 15.1 seconds.
The first thing to do is make a few practice runs through the course to make sure that you're aware of where all of the cardboard cutout enemies will be, as you can deduct up to 3 seconds
off your final time with the accuracy bonus
-- bringing down the time required to 18.1 seconds.
Strategy to get the best time:
Use the MP5 as your weapon (found at the top of the ladders). When you repel down, jump to the right when you hit the bottom. This might take some practice to time it right. Take out the first two enemies, sprint inside the door to the right, and take out the third enemy in that area.
Sprint down the stairs and kill the enemy at the bottom, prepare a flash grenade and toss it into the next room as you turn the corner. Hide behind the wall so you don't get flashed yourself, and then enter the room taking out the two enemies. Move through the door on the left, be careful not to get caught on anything so that it slows you down, and take out the two enemies in that room.
Prepare another flashbang, throw it through the next door on your left. As soon as you throw the flashbang, move to your right exit so that it doesn't blind you. Start walking backwards whilst still aiming your gun towards the room, shoot the one enemy you can see through the doorway, and aim slightly to the right to shoot the second enemy through the wall. Once the last enemy is down, turn around and sprint forwards towards the timer.
If at any point you mess up, pause the game and reload the last checkpoint. Anything less than an almost perfect run will mean your time is too high.
You can see a video of my run where I completed the course in 17.9 seconds and received a -3 seconds bonus to bring my time down to 14.9 seconds below: