You can repair the damaged SD card by replacing the connector on the board. Alternatively, you can try to run a jumper from the pin or solder the wire on the SD card reader pin. If you find the work too challenging, consider buying a new SD card.
Different from repairing corrupted SD card that has logical errors, it's a tough job to repair a physically damaged SD card. Therefore, before hands-on the SD card repair procedure, make sure you are fully capable of handling the micro work ahead.
Replace the missing connector with a new one. You can easily purchase a Nintendo memory card module FPC connector socket. Then start micro-soldering on your SD card.
Trace where the pin goes and run a jumper from it. Since the points are fully exposed on the SD card board, it would be easier to deal with the pin instead of messing with the connector.
Solder the wire on the SD card reader pin to the top-left gold pads. One more option for you is to leave the connector on the SD card behind and work on the SD card reader pin.
Hopefully, you can fix the damaged Nintendo SD card.
