I had a hell of a time on Normal, because I entered the fight with 6 detonator mines and NO OTHER AMMO. It took 3 mines to take out Evil Nicole; the second time I took her out (having as yet done no actual damage to the Marker), it insta-killed the shadow hordes, so I was able to dash around and pick up the ammo they dropped...being careful not to run into E.N. and her insta-kill.
That's clearly NOT the way to do it, so when I went through again on Zealot I had a plan. I stocked up on Plasma Cutter ammo and Contact Beam ammo. (I also had health, but I didn't have to use it -- busted the Marker in 1 playthrough.)
Upgrade your Contact Beam so that it has all the Alts and the Special node covered. (They're all in one path, so it's easy.) Now, when you fire the Contact Beam's alt, it not only wipes out every shadow around you, it also hits everything nearby with stasis. As E.N. comically flails backwards in slow-mo, use your Contact Beam's primary fire on her. It only took me 1 alt-shot and 1 easy primary shot with the Contact Beam to take out E.N.; then I unloaded on the Marker with the Plasma Cutter (which was fully upgraded, as this was a New Game+, but that's not necessary -- nothing even TOUCHED me.)
As of this writing, this is the 4th guide for this achievement, and I don't know why nobody else has mentioned the Contact Beam. It is far and away the best weapon against E.N., because it simultaneously annihilates the horde, damages her, AND hits her with stasis so you can get the easy kill shot. I also found that the Contact Beam's alt was great for getting through the prior chapter; any time you get surrounded, hit the alt and everybody freezes and/or explodes. (I used regular-old stasis and Plasma Cutter on the indestructible creature.) Just make sure you load up on plenty of Contact Beam ammo at your last store stop.