The Donkey Kong cartridge was dumped using a Nintendo game cartridge extraction tool called the Retro Dumper V4, connected via micro USB. The extracted .nes file was then used to verify basic Mapper 0 functionality in Nyxx.
On Gentoo Linux, simply connecting the Retro Dumper V4 via USB allows access to the dumped file as a standard mass storage device.
It is likely that the same process works on Windows and macOS as well, since the device appears as a generic USB drive.
Personally, I bought my cartridge at Book Off, but on Mercari, you can often find nostalgic games for as little as 500 JPY.
If your ROM doesn't work even after multiple dumps, you can try a legendary technique known in Japan as “Foo Foo.”
It may sound silly, but this time-honored ritual has brought many stubborn cartridges back to life — including Galaxian itself. Use with care. While unscientific, the success rate speaks for itself.