This can be done either Solo, Online Co-op or Splitscreen. There are 20 Waves for each map and the number of enemies increase after every 5th wave.
Please be aware that
will stack with the Normal or Rookie difficulty. So you can just start straight on realistic difficulty if you want to.
The maps you need to complete are:
Russian Embassy 1
Russian Embassy 2
Lumber Mill 1
Lumber Mill 2
Lumber Mill 3
Printing Press 1
Here are a few pointers to keep in mind that will help:
You can start from Wave 15 for each map and after beating Wave 20 your achieve' will still unlock.
Find a good vantage point to take out enemies without attracting too much attention.
Stick to a Silenced Pistol and try to pick the enemies off 1 by 1, keep a secondary weapon that you are good with incase all hell breaks out. Preferably a shotgun!
Use the aim assist to your advantage. As you may have noticed, when pressing the right anolog stick to aim, sometimes the cursor will lock straight on to the enemy's head. If you are quick enough you can simply aim and instantly lock on to their head and quickly fire making for a quick 1 shot kill.
Save your 'Y' Button execute for emergencys or for a quick takedown of 4 enemies, can be 8 enemies if your team mate marks 4 soldiers too. But keep in mind when going for an execution or hand to hand kill to gain the ability to execute, you can be annoyingly caught in a chokehold or exposed to 4 or 5 enemies at once. If playing Last Stand Solo, the enemy can't choke you but can still give you a push when you try to execute them. This can give them time to plug a few more bullets into you along with their team mates.
Take your time and keep your aim steady! Its very easy to miss the first shot from a Pistol and then just start trying to spray with it! Leave short gaps between each shot so that the reticule goes back to a small more accurate size. If the reticule goes red it will be a headshot everytime, when enemies are too far away but you are aiming at their head. The pistol can still miss as the range isn't amazing on most of the pistols.
Here are a few videos ive found that can give you a rough idea on how to set up for each map, in the videos he just shows you the first wave of each map on Realistic difficulty.
(Credit to seventj7)
Hope this helps, good luck!