I remember earning this achievement in 11:38. This is an achievement that can be accomplished if you do it quickly.
From the beginning to the area where you have to get into the second elevator, that entire section should be done in complete stealth. So the recommended weapon of choice should be the P99 Silencer. No other weapon will do the trick, except maybe for a silenced weapon like the Kallen silencing machine gun, but to be safe, go with Bond's trademark gun. As usual, you'll find guys near each other sometimes, so kill one with a headshot, unload bullets on the other, or try to get headshots on both.
Also, the drone guns will be of great use in this section. Make sure to use your smartphone on them so that they can kill them quicker. You'll find all of them in the first half until you reach your first set of stairs to climb on.
Once you reach outside, make sure you kill the three guards silently, then retrieve the silent sniper rifle. Starting from the left, begin executing all the men below, making sure that no one is near each other. If you happen to cause suspicion with the last remaining guard, just shoot him in the head quick. Then start making your way down. You'll come across guards that are far away, so kill the one behind before killing the one in front. You'll also come across a lone guard walking from the right side, so either kill him with your gun or do a takedown. It's your choice.
Once you reach the bottom, grab the explosives and retrieve the body armor on the opposite side, near to the left. I never had to pick up the body armor in the first two locations until reaching the third body armor location, which is this one in my first and only playthrough in getting the achievement. In any case, as you approach the first elevator, three guards will come out. Kill them quick before they can fire at you, then take the elevator.
Once you reach your destination, another lone guard will his back turned to you. Take out your P99 Silencer and eliminate him. Then earn more ammo for the sniper rifle, which should be right in front of you. Equip the sniper rifle and start picking off enemies starting from the left to the right. The video guide from above should tell you who needs to be killed first and last. Once that's accomplished, make your way through the right side, making sure to disable the camera.
Once you reach the room inside, the one with a security camera, disable it and wait for two guards to walk out. Kill one with a head shot and run towards the second guy, using a take down on him to finish him off. From there, run down the stairs and head to the second elevator, pushing the button.
The elevator will start to rise up, but you'll have to wait for it while dealing with enemies. Since this is on Classic 007 difficulty, make sure you earned the body armor I mentioned earlier. It should be enough to deal with the damage they inflict upon you. Kill a few of them if necessary, but once the elevator is up, run in and press the button to your left, then crouch. You won't have to worry about them again.
Once the elevator reaches its destination, one guard will be waiting for you, with his pistol raised. Kill him quick, then move on. From that point on, you will be dealing with multiple enemies, six of them, with three guys on the left side and three guys on the right side. Disregarding stealth altogether, use your machine gun and take them out. Once all six men have been killed, run down the stairs and start going through the room, putting in the charges.
Upon reaching the second set of charges, two men will burst out from the left, firing at you. Make sure you anticipate their movement first and kill them with your machine gun, then set the second and third charges. Before coming out, more bad guys will approach you from the left and right. Use excellent cover and pick them off one by one without getting hurt too much. Once all of them have been dealt with, you'll have to fight and kill two more guards who leave the next elevator and enter the room. Before leaving, make sure you pick up the next piece of body armor, the one that's on the ledge opposite of the double-doors that lead into the elevator.
From that point on, this will more than likely be the hardest part of the mission. Starting from where you got dropped off to all the way at the end, when you'll be surrounded by three guys with their guns, you will have to fight a TON of bad guys. The video guide once again comes into excellent play, showing you the locations of where they come in and how you can quickly kill them. I wouldn't just recommend using auto-targeting and cover though; there are trucks and barrels you can use as explosions to kill multiple targets at once before gunning down the rest of them.
Also, make sure you get the last and final body armor, which is in a dark room to your right, where a guard will be hiding behind a box. Just cross the bridge and enter your right, but only do so after killing him and any other guards approaching you. Once you do that, it's all about not getting hit as much and killing them as fast as you can.
If you do everything right, you should be able to earn this achievement by completing the level in under thirteen minutes! I did this on my first try and once again earned it in 11:38! It can be done! It may take a few tries, but once you make it to the end and see the end result, hopefully be under thirteen minutes, hopefully the achievement should unlock. Have fun and good luck!