Best way to level at the time of this post is in Zombies.
Best done solo, as the XP gain is based on Zombie kills in a farming method explained below.
Equip your operator under "gear" to your preferred setup.
Use any double XP tokens you have/would like.
Upon loading in, you will see a timer on the left counting down from 45 minutes. This is an exfil timer.
You want to collect at least 5000 aetherum in order to pack-a-punch your chosen weapon (best bet is an AR with a large magazine) and hopefully upgrade it with the use of Aether Tools that can be found/rewarded from the contracts littering the map (the small blur icons).
Once you have at least PaP your weapon, head to one of the exfil locations on the map (little exit signs with the blue guys) and when you arrive and initiate an exfil, a generous amount of zombies will spawn around you.
The amount of zombies will increase as the timer I mentioned earlier ticks down.
You are going to ignore the exfil chopper. Once it leaves after the countdown on your screen ends, about 1 minute later the exfil will reactivate.
Call the chopper again, kill the zombies again, and so on.
Repeat as necessary.
When you hit 55 you need to load back into the multi-player menu for the achievement to pop.