Let me add to what the others said.
You said you're playing an Engineer and mentioned the drone, so you're playing a human engineer.
IMO they are the ones being able to deal really well with the Banshees.
Of cause Armor penetration is important. So if you have a piercing mod for a weapon, use it.
If you don't have that, yet and you have incedinary rounds or drill rounds, use those.
If you lack those, too, use your Engineer skills (do that anyways) Put a few skillpoints in Overload, and you can strip that barrier off the banshee in a few keypresses.
Afterwards, use incinerate to deal with the armor. threow in an overload after the incinerate to cause a tech explosion, which does some neat damage as well.
And most important fighting Banshees: Keep your distance. Banshees often do instant kills if you're in melee range. Also if you are at a distance, her Nova-blast can't reach you and you can quickly dodge away or hide behind cover when she uses that biotic projectile.
Speaking of Cerberus Guardians - if you have a Armor piercing mod equipped for your weapon, you'll get them downed much easier.Just shoot that shield - they'll not take as much damage as if they turned their backs on you, but they will die sooner or later.
If you have a choice I'd recommend a SMG on that Engineer of yours, since with that, you can also keep pressure on the Phantoms, when they use that shield, that blocks all your tech powers.
Speaking of those - if they are coming after you alone, hit them with everything you have. Wait until they shot three times with their palm gun and then use whatever you have - overload, the drone, incinerate and let that smg run hot. When she hunkers down and uses her shield, use the smg - it goes through the shield.
If she cloaks, look closely and continue shooting her with your smg. If she does not use her shield or is not cloaked, do not give her time to breathe. The moment you stop pressuring her, she'll use her damn palm gun and starts leaping at you to instantkill you. If you need to get your shields up or whatever, blast her with tech, so she brings her shield up. That is the time you can run for cover if you must, but if you can, better keep pressure on her, or she might come after you.
Edit:
Forgot something - if the goddamn Phantom is accompanied by one or two Dragoons, try and drop them first and do it quickly.
They are armored, so your incinerate and afterwards a tech explosion trigered with overload works wonders against them. But often you simply dont have the time for that. If they are in close proximity already, dodge-roll your butt away. Quickly. And hope, teammates are nearby to assist you against 'em.
Hope I was able to help.