The technique I used to get through all these veteran difficulty levels is pretty simple.
All you do is go through and get "trigger happy".
First you need to make sure your AIM ASSIST is turned ON.
From there you need to just rapidly start TAPPING the LT and RT repeatedly when you come across enemies.
The LT will automatically, for a split second, AIM at a given enemy's neck on screen and the RT will FIRE a bullet or barrage of bullets at that spot. If you do it fast enough, the sight will focus only on the enemies on screen.
If you see an enemy or two up close just take your time (if you want) and kill them.
This technique really helps for taking down large groups of enemies that are hidden behind cover with only their heads showing or arms showing.
I would use the trigger technique for every enemy just because some of the AI is broken and "headshot"s you from cover.
If this explanation isn't clear, please leave a comment so I can improve this.