Take out the smaller ones first before moving on to the Elites. Inside the room, you'll see more Jackals and Grunts, potentially a Brute, and for sure two Elites in the back of the room. Use the Grappleshot to hop up to the second floor and approach the next door. If you're playing on Legendary, we recommend picking off any of the Jackals and Grunts you see from the outside hallway before entering the next room on the second floor.
You can use the nearby fusion coil to do some quick damage (careful for the bounces from the hardlight) and proceed to eliminate them. Walk down the hallway and take a left at the end to encounter two Brutes. Walk straight across to the next hallway. If you can't get them from where you're at you can walk through the opening on the left and walk through there to their platform. Some well-placed shots will make quick work of the second three. As you walk forward to kill them you can also kill two more Grunts and Jackal across the gap from your platform. Proceed and you'll come across two Grunts and a Jackal. You'll come to a long, large corridor that's partially broken. Then, once done, use the grappling hook on the ledge above and proceed through the door. The pillar in the middle makes for a good spot to dodge bullets if you need a reprieve. Then you can try to land headshots on the Grunts and Jackals before running in and clearing out the two Brutes. If you're having trouble with this last area, try to get a weapon with range (preferably a Pistol if you still have it from the previous level) and sit on or behind columns that give you a safer look at the battlefield. It's best to try and land headshots on both these Brutes, especially the red one. One is a standard Brute equipped with a Mangler while the other is a heavily armored Brute equipped with a Ravager. Like the previous area, another Banished ship will fly by and drop two more Brutes onto the battlefield. Try to pick off the two sitting up on the ridge first so they don't pester you while you work on eliminating the others. With that set of enemies cleared you can move forward to come across yet another set of Grunts and Jackals. You can also use the Grappleshot to scale the large pillars around and get the high ground, but the Banished can shoot you up there if you're not careful. As always, headshots are your best friend. Be careful not to back up or accidentally fling yourself off the map with the Grappleshot! If you're playing on Legendary, do your best to use the limited cover in the area to avoid taking hits. You'll only get a short window to fight them solo before a Banished ship swoops in and drops off two Brutes. Move forward to spot Jackals accompanied by Grunts. The weapons you had from the previous mission should have carried over, but if you're low on ammo, consider picking up the Elite's Pulse Carbine.
A note about Elites: they get extra aggressive after their shield is down. You'll load into the area with weapons from the previous level, though, so you might just need to land a few good shots to break his shield with whatever you have then finish him off. You can take down his shield quickly with a plasma weapon. When you drop into the Foundation you'll be greeted by your first Elite of the game.