As usual, go in fully stocked with Mika tickets, and if possible, a fully upgraded "Healing" skill (which lets you hold "LB" to trade blood for health -- doesn't have to be fully upgraded, but it makes the transfer go faster).
You will battle forward through a train. In the first section, there are quite a few enemies, so it helps to stay clear of them and shoot for headshots.
In the next room, find Scarlett by activating a panel behind the last bed on the left, then shoot the two wall circuit panels on either side of the forward wall to open the door.
When you reach the room with ramps on both sides and a catwalk across, Scarlett can again be found, in a box up top at one end.
When manning Bryan's turret, alternate between shooting the orbs (which contain turrets that shoot back at you) on the other train section on the right, and the enemies that are approaching. There are four of the orbs to shoot, with one being farther foward and low down, making it kind of hard to spot. After this, you'll take control of a standard turret after that, and there are two more orbs to shoot if you swing around to the right and slightly toward the back. In this phase, there are floating machine enemies, so take them out too as they appear. These orbs take a LOT of hits before exploding, at least on high difficulty levels.
Finally, shoot the four orbs that appear at the front. These don't move, so they're a little easier. Enemies are also coming for you, and it's likely you'll overheat the turret if you're not careful, or they'll just be too fast. When this happens, get off the turret, go forward toward the red room to lead them away, then run back to the turret and shoot again. You can try taking them out the old fashioned way (with gun and katana) but be prepared to take some damage.
If you need it, there are health pick-ups in boxes near the forward section, on the right and left. Break them to collect the gems.
Before leaving the area (don't enter the red room once all enemies are dead), go up the ladder on the right to find Scarlett a third time. You can do this even during the battle, but you're likely to get trapped by enemies on the way down, making it hard to get away.
In the next room, shoot the circuit panels on the left wall and the forward right side to continue.
Go outside, climb a really tall ladder, and get prepared to start crouching a lot. As described in an earlier level, you crouch with LT and click down on the right stick. You don't have to hold the right stick after clicking it down. You'll stand up as soon as you move, attack, or let off LT. (Note: you can also avoid being hit if you dodge just right - move the left stick and hit B, just before going under the railings -- but this won't help in getting the AAA rating for the level). Make your way forward breaking boxes, and crouching before the train goes under the low areas (otherwise you take damage). Look for the final Scarlett of the game in a box about mid-way forward on the right side.
Finally, you'll begin the boss battle. The first phase is fairly easy, if you stay all the way back. This allows you to avoid the eye-tentacles sweeping attack. And you can dodge (with B and moving the left stick) the straight-down attacks, sometimes triggering a dodge burst. Just slice away when you have an opportunity, and stay back against the wall where you came in.
Sometimes a fire will shoot out from the front. Move all the way to the right or left to avoid the flame, when you see it starting up. Then get back to the middle against the back wall.
Each eye stalk has its own health, but only one bar is shown at a time. So if it looks odd that the health keeps going up and down, it's probably because you've dealt more damage to one than the other, and it switches depending on which one you attack.
The eye stalks alternate attacks, so when you're attacking one that just dropped, be prepared to dodge the other one which is coming a few seconds later.
Once an eye stalk has no health, it will do a straight-forward attack at you each time. There is a very brief moment where you can hold RT + X (when prompted) to sever the eye. Repeat the same for the other stalk, once its health is down.
The final phase is a little different. I don't have a foolproof strategy for this, and took quite a bit of damage (and Mika revives) on Very Hard. What seemed to work best was moving all the way forward this time, and just going crazy with the katana. You can dodge some, but it's a lot harder. Even after its health was gone, I had to keep dodging since it would withdraw into the furnace and shoot out violently. At some point -- not sure whether dodging triggered it, or it got tired, or what -- you'll get the RT + X prompt to finish it off.
You can try fighting it from a distance, but the purple stuff it spits then is pretty hard to avoid also.
After cut scenes play, the mission stats will appear and you'll get the achievement for beating this mission.