Good news! It's all smooth sailing for collectibles from here. Only three for each of the remaining levels!
Retrieve the Ark
You'll begin in a huge battle of Titans vs. Titans. This is a good time to get any Core achievements you haven't yet obtained out of the way.
When you get to the wall at the beginning, you'll also encounter many enemy Titans clumped together. This is the perfect time to unleash your Core ability and try to kill three at once. I found Ion to be best for this. While it's definitely possible to get this on Master, it's significantly easier to an easier difficulty so I wouldn't waste time trying to get it. Just come back later - it's right at the beginning after all! If you do manage to get it, you'll unlock an achievement.
Destroy 3 enemy Titans with 1 Core ability in the Campaign
When you're here on an easy difficulty, it's also a good time to hop out and rodeo a Titan if you haven't yet done that. All you need to do is find a Titan that's relatively alone and jump on it as a pilot. You'll do an animation where you tear out its battery and earn your achievement. Keep doing this over and over again until the Titan dies to unlock a second achievement. If you really want to do this on Master, try to single out a Titan without any allies nearby and get it very low. Then run up to it and get out of BT so that you hop straight onto the enemy and kill it in on go.
Rodeo an enemy Titan in the Campaign
As soon as you enter the building, you should see a balcony on your left. Hop out of your Titan and up onto this balcony. Between the two spinning turbines you will find Pilot Helmet (1/3) (38/46) (10:51).
Continue forward until Briggs tells you to get on an elevator. This will be right after you pass two health crates. In the hallway right before the elevator, look to the right and you'll see a little hole in between stacks of boxes. Exit BT and go through the hole. Follow the path to Pilot Helmet (2/3) (39/46) (11:03).
At the top of the lift you'll find the Northstar loadout hanging down from the ceiling. Be sure to pick it up. It shares a Core with Brute so you don't actually need to worry about getting an achievement with it. Continue forward a few steps until you see a gap in in the fence. It'll be between two red tubes. Get out of BT and run down to this walkway. Continue down it and you'll see a very obvious Pilot Helmet (3/3) (40/46) (11:21) sitting on top of an arch.
Now you simply move forward and fight more Titans. And then more! When you get to the ship, you get an achievement.
And that's that!
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