Most of the PEC is easy to get and you probably already have them or close to it. If you're on here I assume you want help in getting thru the harder ones faster. This method I'm about to describe works easily for the following Vanish Challenge PEC:
Portable EMP Escape
EMP Grenade Stun
They can also be done in combination with the following Prepare & Execute Challenges:
3X Frag Grenade
Go to the Security building in the beginning of the White Box Labs mission that has the glass ceiling with the pipe overhangning it and climb the pipe to the window.
The EMP Grenade Stun is the easiest one to do. Simply drop a grenade thru the glass and when the stun effect wears off, drop another. Repeat this for all 3 EMP grenades. Now position yourself so that your head is facing the direction you came from and make sure you have either your portable EMP or your flashbangs ready to deploy, then take out your pistol and fire a shot near a guard but DO NOT hit him. You need them alive to complete the Vanish challenges. As soon as they detect you immediately drop the flashbang or activate the portable EMP and haul your butt out of view back down the pipe. Wait until your health builds back up and your Last Known Position (LKP) disappears. You might want to wait until they stop shining their flashlights up towards that area too. Now shimmy back and turn around again, fire another shot to alert but not injure or kill a guard and drop another flashbang or activate the Portable EMP and immediately shimmy back down the pipe again until the coast is clear. Repeat this for all flashbangs and all Portable EMP until they too are gone. Now hit the pause button and select "Retry Last Checkpoint" and confirm it. You will restart right back outside the security room again to repeat the process over again. Keep doing that until you have been notified that all 3 of those Vanish challenges have been completed.
Sometimes you might be too slow to drop a flashbang in time before they shoot you down. It sucks but it happens. The Flashbangs are the hardest to get thru due to their delay while guards are shooting. Thankfully there are fewer of those to do than the EMPs. If you find it easier try doing it on the Rookie setting instead of Normal or Realistic.