I am not covering how to get the shadow mantle, but if you have it then equip it to Susie. And if you don't, then you probably shouldn't be trying this.
Here is everything I had on my successful attempt.

Kris: Defense is the name of the game here. All your items should max out defense and/or give a special bonus unless Susie could make better use of their magic stat. For swords, Bounceblade is the obvious choice.
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Susie: You are the damage dealer. Obviously you should have the ShadowMantle, but besides that, You should have the best gear stat-wise. the Devilsknife makes this fight significantly easier with it's decreased TP cost for rude buster, but if you don't have it then your choice of axe doesn't matter much since rude buster will be your only attack method.
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Ralsei: Your job is to whack the knight a couple times and then die. You should have the pink ribbon and the tension bow because their bonuses to TP gain and graze area are still active even when you're down, giving you value. If you have the Puppetscarf, congratulations! This is it's prime use case. Ragger2 will suffice if you don't, though. Your damage is temporary, anyway.
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You should have:

• at least 3 revivemints, to be used exclusively on Susie. if you don't have enough you can supplement one with a revivedust, but that will make things harder since Susie revives with less health.
  
• Spincake, the best healing item in the game. Giving everyone +140 HP, this can absolutely turn the tide of the fight if used at the right moment. Don't be afraid to eat it, topchef will give you another if you talk to him at the start of chapter 4. (this was previously not the case, fixed in a patch.)
  
• As many ExecutiveBuffets as you can get. ClubsSandwich also does the same thing but with worse healing, so if you have it eat it earlier in the fight and save the good stuff for later.
  
• Fill the rest of your inventory with DeluxeDinners, or the light candy if you still have it.

Each party member has a very important role to play, but what that role is might not be clear. Major exceptions for these roles should be made for the final 3 turns, which are scripted. See the Turns section for more info.
Deviating from these roles can be a good option if you don't expect the next attack will be much trouble, but it's unwise for a casual player.

Always remember the Pippins' tip:

This nets you around 15 extra damage per rude buster, which can definitely make a difference.


Kris: You are Susie's new healer/assistant, and you only have 3 jobs on your turn. If you are attacking then you're doing it wrong.

• Defend for TP
  
• Heal Susie and yourself
  
• Revive Susie

Susie: Rude bust until you can't, do something else for one turn, then continue rude busting.

• If you have enough TP, use rude buster. Always.* Kris should be healing you if you are low on health, so don't worry about that.
  
• If you don't, then heal or defend depending on your HP and confidence.
  
• *Heal Kris with a non-revivemint item the moment they go down, unless you're near max HP and are confident you can survive another attack to use rude buster this turn.

Ralsei: Your goal is almost exclusively to whack the knight with Susie for as long as you can. Do not heal yourself except with whole party healing items. You will absolutely die at some point in the fight. And you should absolutely not be revived.

• Attack.
  
• If you're still standing and the other two are badly hurt, assist Kris with healing USING ITEMS ONLY. With this strategy, TP is only barely not a concern most of the time, so wasting some on casting heal prayer means that Susie spends fewer turns rude busting and thus the fight goes on for longer, which is very dangerous.

Other people can provide footage of their moves, but their moves are so fast, luck-based, and difficult that visual knowledge can only go so far. Also, I got hit dozens of times by the knight on my successful run. It's definitely something to avoid as hard as you can but a single turn should not do you in. The only turns worth talking about in detail here are the first one and the last three.

First
Kris Defend, Susie Attack, Ralsei Attack.
Luckily, the first attack the knight uses is the easiest to dodge, so you get a free round to pile on damage and gather TP.

Last
You'll know you've gotten to the end when Susie says this dialogue:
If you've been doing good damage, then you should be either at the final phase, or only one or two rude busters away.
The last 3 turns are easy to plan for.

-3: You get one completely safe turn to heal up with whatever items you have left. Do not waste time attacking or defending with either character. Both Kris and Susie should use healing items. Nothing should happen on the knight's turn.

-2: The knight will begin glowing. this is the indicator for their final, screen-wide attack. Once again on this turn, attacking them is useless.

Kris should use hold breath in the ACT page for bonus movement speed, and Susie should heal herself or Kris if necessary.
as pagafantator said in the comments, this final attack ignores any armor or defending. While I cannot test this, if it is true then I agree with them that going against the rules and reviving Ralsei with Susie would be a good idea. However, this still consumes a revivemint, which is a hefty price for a couple more hits to tank against an honestly not that difficult to survive attack. (at least relative to the baseline difficulty of the fight.)


-1: If you survive the final attack, you're home free. Stab, slash, or rude bust the knight one last time to finish the fight and claim your well-earned shadow crystal.

If you can take this advice and show the knight who's boss, I'll recognize you as a certified epic gamer. And I hope you did all the other secret BS too, or else you'll have to fight them all over again.
Thanks to pagafantator for their advice in the comments, genuinely had not thought of that strategy, and Thank you for reading!