There's not a great deal I can offer you in terms of how to get this achievement, it's all in the description, complete this portion of the game on Veteran difficulty, however you may find these video of the mission handy, it'll help you get your bearings on any part you might be stuck on and give you an idea of what to expect!
Also, remember to stay in cover and progress slowly, sometimes it's hard not to but try not to rush around, you're much more prone to make a mistake or run straight into an enemy and wind up getting killed and having continue from the last checkpoint, the game can get incredibly frustrating at points so be sure to take breaks from it if you need to, go and clear your head, calm down and come back to it feeling refreshed and ready to beat it, it's not good tearing your hair out over a certain section and continually trying it, the more frustrated you get the more likely you are to make a mistake.
* Credit to WoopzillaWalkthrough for the videos