Mass Effect 2

This one is unmissable, but i'll try to keep it spoiler-free. The enemy is tough, she'll use biotic waves to knock you out of cover, so listen for Liara calling them out. The enimy has a biotic barrier, armmor, and health. And after taking down half of the biotic barrier, she runs off and more eclipse mercs and rocket turrets. Use the cover near the back, and watch out for the rockets. After taking them out the boss will come back. Careful for when she uses a biotic move that lets her jump around the map, so she could get you from any angle. Try to keep your teammates alive for as long as possible, and dont go for close quaters attacks, snipe her out. When shes in the open, Liaras attacks work great, so take that oppertunity to get in a few golden headshots.
This may take 7-13 minutes on average, but she's basically just an upgraded Asari Vanguard.

Insanity Guide (I played as Sentinel class)

The availability of Stasis power can make this battle almost trivial.
Max out Liara's Stasis until you reach Enhanced Stasis. Liara's Warp power is also useful for destroying Barrier.

Stasis is unique among all the powers in that it will work despite any defensive layers that an enemy has (including barrier) - knowing this you should use Stasis repeatedly on this boss. She will freeze in place and can take no damage, so there is no point in shooting her yet.
Once Stasis wears off, she will fall to the ground briefly, where she will receive bonus damage (x3 to x4). As she is getting up use this small window of time to shoot repeatedly and fire warp at her.

One she stands up apply stasis again. Repeat until you beat her.

Hardcore Guide

I played through on Hardcore as a Vanguard so you might find tactics that are more effective for your build, but hopefully what I say will still be of some use. I'll keep things as spoiler free as I can by only referring to the boss as "it" or "The Assassin."

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Soldier Tip:
"As a soldier I found bringing Garrus or Kasumi was really helpful to bring some balance to the team. You'll need some solid anti-tech."
Credit - Old Willy Pete
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Phase I:

This is a mostly long range battle where patience is the key. The Assassin will randomly teleport around the area and try to pick you off from a distance. Do your best to be aware of your surroundings and adjust your cover as needed. Return fire with a long range weapon whenever you have an opening. Your allies will likely be quickly picked off by The Assassin. I don't recommend reviving them during this part of the fight. They'll most likely just get taken out again and you'll want to save your medical supplies for the rest of the mission.

The Assassin will often send a shockwave your way. Whenever she does so, be prepared to leave your cover, get out of the way, and then return to your cover. If you do this fast enough you should take little to no damage. If you get hit by the shockwave The Assassin will land some hits on you and possibly kill you.

If you see The Assassin standing still while charging up biotic energy this means that you're about to get hit by a Charge attack. Switch to your shotgun and start strafing. Regardless of whether or not you get hit you'll probably be able to get in a hit or two before The Assassin teleports away again.

Phase II:

Once The Assassin takes enough damage you'll be left alone while some generic enemies and rocket drones come in. This would be a good time to revive your party so you don't get overwhelmed. Use Liara's biotics (and your own if you have them) to disrupt enemy humanoids whenever possible, and focus any shield disrupting skills you have on the rocket drones. Once these enemies have been defeated you will return to Phase I. The two phases will alternate until the end of the boss battle.