Yeah thats right about the other achievements being for completing levels on Veteran difficulty, but for "War Hardened" you only have to complete the game on Hardened difficulty (which is one difficulty level below Veteran).
By completing on Hardened diffculty, you will only get the achievements "Won the War", and "War Hardened" worth in total 350GS, but it is slightly easier if you cant quite handle Veteran!
On Veteran as above go slow, take your time, and in open areas use smoke making sure you dont use too many and run out - as this can be the difference between a section being fairly easy, and almost impossible.
Use cover where you can, if you start getting hit drop to prone ASAP as this can save you sometimes, but most of all keep moving forward! The enemies will infinately respawn unless you get past a certain point to trigger them to stop. If you stay too long in one position it is very easy to get pinned down, so take it steady - but keep moving!
Always have one bolt action (or any rifle - M1 Garand and Lee Enfield being the better ones) and one machine gun (MP40 is good and you will find plenty of ammo from the dead Germans) in your possesion. The rifles are excellent for picking off targets in the mid-long distance, and will kill in one shot. Use the machine gun when clearing houses, as you often need that extra power close up (however they are useless at mid-long range).
Also use the auto aim to your advantage if you have it turned on. Aiming your crosshair close to the target and pulling the left trigger (to use ironsights) will snap you onto the poor guy, so you know you can fire as soon as you pull LT and you will kill him. If there are a group of enemies in the distance, aim your crosshair in the middle of the group, pull LT, fire, let go of LT, pull LT, fire, etc etc and you will keep snapping to the next guy without having to adjust your aim.
Grenades are useful for clearing houses, but also for "charges" through smoke. After throwing a smoke grenade and waiting for the smoke to obscure their vision, cook a grenade and toss it far forward into the path where you are running. This will take out any guys that otherwise you would run into and gun you down.
Take advantage of your teammates! They are unlimited in number so dont worry about them too much. If you are stuck at a section, wait for a lull in the enemies fire and make a charge for a decent bit of cover as close as you can to their position and go prone. Your teammates will advance with you, and although many will get shot - it often happens that your new position has trigged the AI to stop respawning there. Whilst you are face down on the ground your teammates will eventually mop up whatever enemies are left, leaving you free to stand up and keep advancing!
The levels are fairly open, and most have multiple ways round the enemies position - so if one way isnt working out for you, try another. You may find it easier than the way you were trying for so long!
Most off all on Veteran difficulty this game can be VERY frustrating. If you get stuck on a section over and over again - put down the controller, turn the game off, and come back tomorrow with a fresh head. You will often find that the section that was giving you so much grief the say before you can now quite easily stroll through. When you get as frsutrated as you do playing this game - you start rushing and taking silly chances, which of course only makes things worse. So turn it off, take a breather, and come back with a clear head the next day.
Easy, huh?!? Good luck!