When you load the Game up, Select 'Campaign'
Providing that you have completed the Story already select 'Replay Mission'
From this Menu, you can select Which mission you want to play.
Select the Mission you want and Change the Difficulty to 'Veteran'
This Menu, you can Change your Loadout to whatever you want.
I suggest using the: Storm PSR
M8A1 - Attachments: Milli Scanner
Perks: Access Kit
The reason why I suggested the Storm PSR is so that you can Hide behind Cover where you are safe from Enemy Fire, and yet you can still kill them. The M8A1: So you can quickly 'Snap' onto Enemies at Short/Medium Range. (Using LT to aim, and RT to fire) Whats also good about the M8A1 is that it is Burst-Fire, Keeping the Recoil to a minimum! :)
Take each level Slow, Making sure that you use the M8A1, and Storm PSR effectively. Before advancing to the next area, Make sure all Enemies have been eliminated.
The Levels/Missions you need to complete for this Achievement are....Celerium
To check which levels you have completed on Veteran Difficulty, At the 'Replay Mission' screen...Press 'X' to view your 'Combat Record', On the 'Overview' tab, Select the Mission you think you may have completed, and at the bottom of the Screen (Where it says 'Difficulty, Challenges, Robot/Vehicle Kills, Explosive, Stun) Under 'Difficulty' you can see what missions you have done on Veteran.
Please comment what I can do to make this Solution better before voting Negative....Thanks!