Well this mission's certainly going to go out with a bang.
Survive
BT will give you an old favorite weapon. Once you have it, hack the control panel next to the windows to leave. In these hallways you will encounter groups of enemies that you Smart Pistol will make short work of. This is a fantastic place to get two achievements - one for killing three enemies during one slide and one for three enemies in one wall run. You slide by pressing 
while sprinting. So simply slide or wall run while enemies are targeted and press 
to get these achievements very easily.
Once you exit into the daylight, Briggs will let you know you can call in a new BT and set you a waypoint to do that. Kill the enemies in this area (there will be a turret in a shuttered window you can't kill. On the left you'll see some black tubes going up. On top where these black tubes go is a pilot helmet. Scale the wall to the roof of the building with the turret and then jump up to the top where the black tubes go to get Pilot Helmet (1/3) (44/46) (12:25).
Now jump down to the other side of the building and press 
to call in a new BT.
And if you've been following along and this is your last loadout (Legion), you'll get an achievement. If you didn't get them all for some reason, reload this mission once you're done and you'll have all the default things the game thinks you should have at this point (including every Titan core). Run back to here and it will pop.
Get to the Fold Weapon
The next are has a ton of Titans. Make sure to kill one of them with your Smart Core, which is awesome, to get the final Core achievement.
Continue on until you get to a point where you go inside. The building is labeled B4. As soon as you walk inside, look on the ceiling near back and you should see a familiar blue glow. Run to the back, get out of BT and jump to get near the ceiling and wall run over to the pipe on which you will collect Pilot Helmet (2/3) (45/46) (12:44).
Now reload the checkpoint. We're going to get another achievement for killing 25 enemies in two seconds. Your objective is to the left. You'll need to crouch and walk down a hallway with dozens of enemies. Walk slowly so that all the soldiers get bunched together at the end as they run away from you. Make sure not to step on them. Once they're all grouped up and you think you have more than 25, unload on them with your minigun. If you have your Legion Core, that makes it even easier but it's not required. You can see it done in the video below.
At the end of your hallway you'll turn a corner and enter a room with a bunch of Halo rings in it. In this room, you'll turn left and go up a ramp. From here, you can look in the back left corner near the ceiling to see the final pilot helmet. Jump out of BT and then wall run on top of the building with the glass windows. From the roof, jump on the pipes against the back right wall and then walk along them to reach Pilot Helmet (3/3) (46/46) (13:07).
If you've been following along, breathe a sight of relief. That's all of them!
Now it's a fight with Slone. She has a very powerful Laser Core, so always be near cover and run from that as soon as you see it charging. Always focus on the extra Titans first. She starts with a Brute. At 66% health, she will phase shift away and spawn two Tones and a Scorch. At 33%, she will spawn a bunch of Reapers. I found it easy to use Legion for the entire thing.
If you haven't yet, Slone is very easy to get an execution on. When her health bar turns yellow and black (once you've depleted it), run over to her and click 
to begin an execution and get that achievement. You'll also get an achievement for killing Slone.
You'll get another cutscene and then your final platforming section. Completing it earns another achievement.
And finally, an achievement or three based on the difficulty you completed the game on.
You did good work! Clean up anything on Easy that you need to and wrap up the multiplayer if you haven't already and you'll have finished the game.
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