I decided to skip playing in order and went straight to the last level. I got all the way to the end, but haven’t yet beaten the final boss.
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Eric Hodel has written 3 entries about this goal
Plasma pistol + battle rifle. If you fire a changed plasma pistol at long range (it homes) you have just enough time to switch to the battle rifle and finish them off with a burst or two.
I haven’t tried this against an Elite, but they should be about as tough.
(I got worked over with the combo playing one-on-one.)
Co-op play helps out alot to figure out where/when the enemies come from, and how best to strategize. I’ve finished all the missions solo as well.