I've included details about each fight/Verse in the description, please read for more details:
Very difficult gimmick chapter. Still not as bad as Route 666's motorcycle ride, though. To fire rapidly, mash the Shoot and Punch buttons together (hit them both with your thumb rapidly). Or better yet, setup a rapid fire controller and spare your thumbs! Note that for demonstration purposes I played this entire run without the benefit rapid fire.
Dodges can be chained together for non-stop invulnerability so if you're in danger, just mash dodge until there's an opening.
This chapter's hell for people with motion sickness, and I have a few friends who struggle with it. I showcase a run that minimizes dodges, showing how to evade enemies without needing to use the dodge button. This took a good 25+ retries to record.
Make sure you go into this chapter with a Gold Moon Pearl and Eternal Testimony equipped if you can. It really helps to be able to keep firing missiles.
Verse 1: The hardest waves are the Decorations that shoot when they're at the end of their flight path. The ones that start far off in the distance end up firing very close to you and are hard to dodge, so make sure to kill them all as they appear.
Fortitude is much easier if you use the dodge button to avoid the shots, but circling around the screen is definitely doable too.
Verse 2: I didn't know at the time how to deal with Kinships without dodging, but you can actually just hide at the top of the screen in the horizontal center where there's a blind spot in their beams. Temperance is way too hard to avoid without the dodge button, so I use it liberally there.
Verse 3: While it took a ton of chapter restarts to make it to Verse 3 without taking damage, the first time I made it to Jeanne I managed to kick her ass. :3
Kilgore hands + Bazillions on the feet. Rockets are amazing for keeping her staggered, and I use Bazillions here because I was afraid of a combo drop ruining my fight. She can't block the Bazillions shots, so any time you dodge you can fire them (get in the habit of holding punch or kick any time you dodge and you'll rarely see combo drops happen if you've got some guns equipped).
The rocket fights are tricky due to the camera, but we get through those quickly enough. The last fight gets a bit dicey when I suddenly realize I'm low on magic. I break open some of the patio furniture for some recovery, and I end up finishing off Jeanne with Pillow Talk charge slashes. I figured my combo was high enough I could get away with using it.
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This Bayonetta playthrough features the secret character "Little King Zero", who is unlockable by clearing the bonus chapter "Lost Chapter: Angel Slayer". Little King Zero is the hardest character in the game to get Pure Platinums due to his innately equipped Infernal Communicator interfering with the use of both Pulley's Butterfly and Sergey's Lover. His minor advantage of very slightly faster running speed and slightly improved magic gain per hit (mostly noticeable when using Scarborough Fair, Handguns, or Bazillions) do not make up for these disadvantages.
This playthrough gets a Pure Platinum (no damage taken in combat, Platinum rank time and combo on every fight) on each chapter while showcasing all the cutscenes as Little King Zero, without ever resorting to the checkpoint restart exploit. Most playthroughs on KZfaq resort to this exploit, where you can immediately pause the game, select Quit to Title Screen, and then Continue to restart any fight where you get hit, or if you're worried your combo score or time are too low to get Platinum. It's easy to spot the jump cuts in Pure Platinum runs where players resort to this exploit before difficult fights. It's especially weird when they deliberately avoid the use of specific weapons or accessories (usually Pulley's Butterfly) in order to look hardcore, but then resort to this incredibly abusable exploit to get their Pure Platinums, which essentially removes most of the stress or tension from having to avoid taking damage while nailing combo scores and time in each fight.
If you can just restart any fight you fail, rather than having to restart the entire chapter, it's far less challenging to Pure Platinum the entire chapter. All it takes is to retry the fight over and over until you get through it without taking damage (and hopefully get Platinum combo score and time) then use video editing to cut out the failed attempts. Lost Chapter: Angel Slayer doesn't allow for mid-chapter restarts, hence why players who resort to this exploit to get their medal screens full of Pure Platinums tend to have trouble with this endurance chapter. The only other player I know of who has recorded a Pure Platinum playthrough of NSIC without using the Continue Exploit is a highly skilled Japanese player by the name of "tomatyesc", who also has multiple recorded Pure Platinum runs of Lost Chapter: Angel Slayer: / tomatyesc