This guide will show you how to get the pieces of clothing pertaining to the sets that are labeled within the wardrobe (see the screenshot below). For the rest of the clothing, you'll have to get them from random drops. Keep in mind some of the random drops can include pieces pertaining to sets, although they will be within a fixed set of boxes.
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Disclaimer: I do not own every piece of clothing as of writing this right now. I'll update the guide as I get more pieces, if necessary.

On floor A3, there's a vending machine where you can get clothing from in exchange for cash. Here, you can get the specific pieces of clothing from the followings sets:

• Lace Bundle: Black, Magenta Corset | Stockings | Panties | Garter Belt (2 variants) | Bustier/Bra variants | Neck Ornament | Briefs | Fingerless gloves | Sheer arm sleeves
  
  
• Police Set: Crop Top | Belt | Shorts (VERY short)
  
  
• KPop Set: Baggy pants | Shorts | Magenta briefs
  
  
• Chinese Set: Leopard Print Cheongsam | Purple Cheongsam | White Cheongsam

The following pictures show you the location of floor A3's vending machine, as well as its interface. Keep in mind that there are other vending machines in different floors, but they will not sell clothing.

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There's a vending machine in front of the elevator on floor B1. As of right now, it contains the same clothing contents as the A3 vending machine, which are listed above. You can see its location below:
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Note that this vending machine did NOT include clothing sets prior to version 0.5.1.

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The Lace Bundle can be acquired, for the most part, through the A3 and B1 vending machines mentioned in the previous section. The rest can be acquired via random drops EXCEPT for the white wedding/swimsuit set - these can be acquired within specific boxes in NG+:

• Veil: B2 basement, room in front of the elevator.
  
• Bikini(?) Top: Bloody room in A1. To get here, you must: take the elevator, put something on a pressure plate, then go through a vent.
  
• Bikini(?) Dress: Save room in floor A5. The room is called "A5 Lounge" and is near the elevator.
  

You can get the rest of the parts for the wedding dress set by collecting tokens and destroying skulls in story mode. The tokens give you the gloves and the skulls get you the stockings.
The list will be updated as I find more parts. If you know where the rest are, please contact me!

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The police uniform set can be acquired in the A3 and B1 vending machines and by clearing the Centralized Control Area challenge. Difficulty doesn't matter.
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It's also worth noting that this challenge, among others, includes random clothing boxes drops. If you're interested, I got the following drops (they've got a red mark) during my latest run:

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Can be acquired from the A3 and B1 vending machines and by clearing the Shooting Range timed trial. Unfortunately, this trial does not have clothing boxes.
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The Bunny Girl Suit set can rarely be acquired from random drops. You'll mainly want to get it through 2 challenges:

• Testing Grounds. Difficulty and door do NOT matter. This one includes random clothing boxes!
  
  
• Desperate Weepers. Difficulty does NOT matter either. Doesn't include clothing boxes.
  

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The KPOP Set can be obtained from the A3 and B1 vending machines (limited set of pieces) and by completing the Abandoned Hangar challenge. This challenge also has clothing boxes in random and fixed positions, including one near the end which will always give you the same piece. You can also get some pieces from random drops.
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The Witch Set can be obtained by both picking up clothing boxes in the Nightmare Castle and by clearing it. This one has a bunch of variants!
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The Demon Suit set can be obtained by clearing the new game mode: Night at the Graveyard. In this game mode, a pink-colored bubble containing a clothing box will spawn for every 15 zombies you kill.

This clothing box will include a random piece from the Demon Suit set. You can pop this bubble by shooting it, throwing weapons at it, or attacking it with any melee weapon. The bubble looks like this:

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The waitress set can be obtained by completing the Fast Food Restaurant challenge. You can do it pretty quickly by getting armed, activating all generators and defending the ones that have the most zombies on them. When time's about to run out, go to extraction to save some time.

I also don't know what to wear the apron on top of, I'm sorry. Unless...
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I hope you found this guide helpful! It's technically a work in progress, since I'm still getting clothing pieces myself. If you'd like to help me build this guide with pieces that can only be acquired in certain spots, like the white lace garments, feel free to contact me. This guide will be updated as more clothing sets are released.

By the way — I'm aware you can use mods to unlock all sets. I personally like unlocking all things myself and being surprised at what I get, one at a time. I know there's more people who enjoy that feeling as well, which is why I made this guide.