OP already asked for help here. I posted a general outline in what to do, but I guess that's too vague to go by. Posting this detailed tutorial in case anyone else runs into the same problem.
How to recover your 3DS SD card by transferring files to your computer using wireless FTP because Windows refuses to recognize the card and wants to reformat it. *
* Internet access and stable connection are required for both computer and 3DS sharing the same router. The 3DS must be hacked with Luma3DS custom firmware.
Take a second SD card and reformat it as FAT32 + 32 KB cluster size. Use guiformat if it's bigger than 32 GB.
Unzip the archive found here to build a test custom firmware setup. Place all the files onto the card.
Boot into GodMode9 by holding the (Start) button. Go to [0:] SD CARD ( ) and navigate into the 3ds folder.
You should see a 3DShell folder. Press (Y) on it. In the bottom screen's top right corner, you'll see [CLIPBOARD] ... 3DShell if it's selected.
Back out with (B) and go into [1:] SYSNAND CTRNAND directory. Press (Y) > Copy path(s) > combo buttons. You should see a copy of 3DShell folder.
In case you've never used Rosalina Menu injection for homebrew launcher, go back and do the same thing in copying boot.3dsx found in the root of [0:] SD CARD ( ).
Turn off your 3DS and swap out your 2nd SD card for your main one. Turn it on again and boot back to GodMode9.
Go into [1:] SYSNAND CTRNAND and press (Y) to clipboard select 3DShell folder. Go back out and then go into [0:] SD CARD ( ).
If you don't have a 3ds folder already in place, hold the R-shoulder button and press (Y) to create a folder. Name that folder as 3ds.
Go into the 3ds folder and press (Y). You'll want to choose Move path(s) as this cut and paste the 3DShell folder onto your SD card (ie removing the folder in CTRNAND).
Do the same thing in moving the boot.3dsx from [1:] SYSNAND CTRNAND to the root of your [0:] SD CARD ( ).
Verify that the 3DShell folder and boot.3dsx file are not in your [1:] SYSNAND CTRNAND. If they've been removed, turn off your 3DS and set it aside for the time being.
On your Windows computer, install the program WinSCP.
If you have no prior experience in using Rosalina Menu's Homebrew Launcher injection, please watch this video to familiarize yourself.
Launch the Homebrew Launcher and select the 3DShell app. Press the FTP cloud icon. You should see this screen.
Start the WinSCP program on your Windows computer. A Login menu should pop up. Select New Site. The login fill out information should be the following:
File Protocol: FTP
Encryption: No encryption
Host Name: 192.168.1.69
Port Number: 5000
User Name:
Password:
Leave the User Name and Password options blank.
Press the Save option and have the Site name: as something unique, like 3DS. This will save a Login profile.
Press the Login button in WinSCP. Leave the Username: fill out as blank. Press OK.
Find a suitable empty folder directory on your computer (left) for you to copy your 3DS stuff (right). Highlight select everything from the 3DS. Drag and drop these with mouse going from right to left. This will copy all the contents from your SD card over to the computer. Make sure your computer has enough free space on the hard drive to complete the data transfer.
If you have a spare SD card that has the same or larger capacity as your main card, reformat the card in FAT32 + 32 KB cluster size (guiformat).
It would be unwise to reformat your main card in case the wireless FTP method doesn't work out for some reason.
Check the empty card with H2testw in a Full Write + Verify test to ensure there are no hardware defects on it.
If the card passes without any problems, copy your 3DS setup over onto that card. Check if all your games and saves are intact.
Side Notes
If for whatever reason you can't copy an exact working 1-to-1 setup with this method, you can do a minimum recovery by backing up your saves using Checkpoint and/or JKSM. Transfer those backed up save data to your computer. Restart all over again in reformatting the card, reinstall your entire 3DS title library, and restore the saves with those homebrew save managers.
If you don't have custom firmware on your 3DS, you're going to have hack it first before attempting this method. Check out the 3ds.hacks.guide for information.
If installing custom firmware is not possible for whatever reason, try your luck with a variety of Windows recovery programs. Here's a reference list to aid in your search:
If the free edition of Recuva doesn't work for you, I personally recommend EaseUS Data Recovery Wizard. The free version has a trial limit of 2GB recovery; either buy your own copy of the software or obtain it some other way.
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