Burstone Quarry is a fairly eventful level: lets you move fast but also requires you to be very precise about it, has a boss fight and a Shard, as well as triggers an invasion of the Ura after returning to the Bastion.

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Overview

The first two gates can be either clipped through from their right side or, in NG+, destroyed with one Scrap Musket shot.

The majority of the level from here on out is very movement heavy. The way will be sometimes "blocked" by a Pincushion, but it is possible to get around them with some careful rolls(or destroyed with attacks, which is much slower). There is a lot of stones all over the level that can cycle their positions when you activate switches that are also spread around, but it is recommended to not use any switches at all - it is not hard at all to roll past all of the stones without activating any of them.

NG+ - some small parts of the level can be skipped with two easy pike vaults.

Eventually you will reach the area where to progress you will have to defeat the boss of this level, Mr Lunky.

Killing Lunky

360 DROP IT

NG+ - in NG+, this boss is very simple. Just attack him with Pike thrusts(which, at full upgrades, penetrate armor). If you crit, you will kill him before he jumps, and after one jump otherwise.

NG ASL - an alternative to the Lunky Drop, only available in NG ASL, is killing him with Werewhisky Hand Grenades. It's very easy to activate Werewhisky on Pincushions on the way through the level without wasting time. Remember that you have to stand behind Lunky to damage him with the Grenades.

The MLG Lunky Drop

In NG categories, by far the fastest way to kill this boss is a quick-kill trick called the Lunky Drop. Basically it involves manipulating Lunky into landing near an edge of the level, and then pushing him off with the knockback from a Scrap Musket shot.

The most common, and a very consistent setup for the Lunky drop can be seen here: Haosedge's MLG Lunky Drop

An obligatory instructional video on executing the MLG Lunky drop: MLG xXx_Sir_Lunky_Drop_xXx Please understand.

Completing the Quarry

After killing Lunky walk over to the first gate at the bottom of this space. Stand in front of it, waiting for it to open(you will also lose the ability to roll). When it does, walk down, open Zulf's dialogue, close it right after opening, and then wait for the switch on the left to activate. Immediately use it. This will start raising the cage, letting you pick up the Shard when it's about halfway raised. You can now leave the level, but you will now have triggered the Ura Invasion.

Ura Invasion Skip

After completing Burstone Quarry, you will be taken back to a ruined version of the Bastion, under siege by the Ura. The "intended" way to deal with this is to fight the Uras, but it is possible to skip this entire(very long!) section almost entirely with this sequence of steps:

1. Die to the Uras.
   1. If you don't have the Cham-pain, use your chance to Carry On and die to the Uras again.
2. Select Restart Level on the death screen.
3. After the level restarts, press Escape and select Exit to Main Menu.
4. In the Main Menu, select Story and then Continue.

After continuing you will finally land at the usual, fully-functional Bastion, where you will be able to store the Shards.

NG+ - Executing this skip triggers the History Books appearing in the Bastion.

Ancient Knowledge

It is possible to get to Lunky's arena with a pike vault or with a jaunt, but it doesn't accomplish anything because this way you won't hit the trigger that spawns Lunky, who you have to kill to be able to progress.

getting through gates