The Golden Path achievement can be quite troublesome, an enemy threat is someone who is aiming at you regardless if they are a hostage or not. On the ground floor in the living room there will be three enemy threats, take care of them with one bullet each.
Then on the first floor you will encounter an enemy holding a hostage captive. You will need to shoot the hostages taker in the left shoulder, the hostage will then be freed but will try to grab a gun. You will want to let her grab the weapon before you shoot as she is not an enemy threat before she does this. The last enemy is in the small room on the right side, simply open the door, let him shoot the door a few times then take him down.
On the second floor you will want to let Alpha 3-2 get downed. After he’s down throw a flashbang through the door to stun the enemies. Then look through the holes in the door and shoot the enemy that’s in front of you. The next enemy will either be behind the settee or on the right corner of the room. Take care of him, enter the room a turn immediately left as another enemy will come charging through the door, take him down and it’s 2 enemies left.
On the third floor, you will open a door to a woman and her child. Ignore those two and proceed through the next door. After you open the door immediately go prone and wait the head of the enemy threat to appear from under the table on the right side, take him down and there’s only 1 enemy left.
The last enemy threat is encountered after Captain Price open’s the last door. You will need to wait until Captain Price says “Drop her”. As soon as he says that take her down, if you fail you can always revert to last checkpoint.
I had a bit of trouble with this achievement, I hope this helped you out.
If you are still struggling, feel free to use this as a reference.Call of Duty: Modern Warfare Wall Hax & Golden Path Achievement Guide