More times than not, there's no reason to push in. Optimally, this means that you'll be using 1-2 rounds on Grunts and 2 rounds on Jackals. Always aim for the exposed hand on the left of a Jackal shield, then tap them on the head while they're reeling. Tap grunts on the head once or twice and they die. Use headshot weapons for all the normal infantry.If they're out of range for the lock-on (the reticle isn't red), then simply fire the plasma pistol as fast as you can and pepper them until their shields pop or you can move up.If you don't use this combo, you'll be wasting ammo and time on Elites, both of which are valuable on legendary. Whenever you encounter an Elite, dip behind the nearest cover, charge your Plasma Pistol, pop out and shoot them, then quickly switch to your headshot weapon and tap them once on the head. That means a DMR, Needle rifle, Magnum, or hell, a Sniper Rifle.
And always carry a weapon capable of an instant headshot kill in your other slot. There's no reason not to, and you'll just be making things harder for yourself by not doing it. Always carry a Plasma Pistol unless I specify otherwise.
