I've included details about each fight/Verse in the description, please read for more details:
Verse 1: Hide by the chest to avoid Jeanne's constant attacks, and beat up the angels.
Verse 2: I find it best to hide at the side of the ramp to avoid the crates once you're at the top here. Gracious and Glorious can be cheesed with feathers as per usual thanks to the high ceiling here to avoid the risk of being hit while building a massive combo. The flaming Ardors are more troublesome as it's easy to accidentally smack one if they get close. If you build up a big combo early on you could use double Durga Fire to avoid this, I guess.
Verse 3: Nothing special, rocket barrages make it easy and keep the Ardor stunned.
Verse 4: Flaming enemies. Use Gaze of Despair to distract them and keep your body safe, and then it's not too bad to deal with.
Verse 5: Competes with Chapter 1, Verse 6 for the easiest Pure Platinum in the entire game. :P
Verse 6: The wind is tricky to deal with and you have to watch out for the fan blades. If you forget to move through the fan blades on Normal or Hard, you can just use Pulley's Butterfly after the fight to get past them here. :)
Verse 7: Silly gimmick Alfheim. Time's pretty forgiving, but you'll only get substantial Witch Time from her Wicked Slice and her full charge sword unleash. Easy, because you can restart any time you take a hit or are worried about time or combo score.
Verse 8: One of the most fun Jeanne fights in the game, namely because the camera isn't terribly silly here. The wide open arena makes it pretty manageable. I ate a hit here once and had to restart the chapter, ah well.
Verse 9: The last two Verses are EXTREMELY tough on NSIC to Pure Plat. I use double Durga Lightning at the start to avoid the electrified water damage. For the last Ardor, I build up as much magic as possible for Verse 10.
Verse 10: Very, very hard. The PC version of Bayonetta doesn't show the water correctly so it's hard to tell how high it is, but I can tell you it rises very fast up to a specific spot high up. The easiest way to deal with this here is to use Bracelet of Time, and use it while carrying Cereza to avoid the Harmonies, set her down at the top of the shaft, then get to fighting.
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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. The people who use this exploit to get Pure Platinums often won't mention it explicitly in their video description, and you have to figure it out yourself based on the presence of jump cuts in the chapter. The worst part is this exploit is useless for teaching you consistent combat strategies. 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