Despite its rarity and high number requirement, this is not a hard achievement to get. You can do this pretty easily without having to replay the same missions over and over again.
E-Turner shows up as small, black and gold boxes. It can be acquired from several sources:
1. Enemy loot drops. It appears the enemy has to be killed by Joule's gun or by your corebots; extracting the core doesn't cause them to drop E-Turner.
2. Destructibles in the environment. This includes the rocks with cracks that glow red/orange/yellow fissures, crates, and cannisters.
3. In chests. This is not common; most chests contain blueprints, but some do have E-Turner.
4. Stand-alone. This doesn't appear to be too common, but some places, like the Warren, are full of this.
All of these sources respawn except for the chests. So as you're playing along on other objectives, be sure to shoot the destructibles in the environment and kill enemies without extracting their cores, and you'll get the achievement eventually.