This mount is easily the most overpowered item you can get early hardmode, and getting it will make the rest of Master Mode a lot easier.
What you need to do is farm Pirate Maps from the ocean biome, and then set up an arena that allows you to kill the Flying Dutchman insanely easy.
Summoning the Pirates
In order to spawn a Pirate Invasion, you need to get a Pirate Map that drops from enemies in the Ocean biome. To farm them efficiently, you need to increase the enemy spawn rate so you can improve your chances of getting a map.
What I do is place wooden platforms over a section of ocean, and put some below that so I can sit in the water. Ocean enemies will swim towards you if you’re touching the water, so it’s best to stand in the water without it being over your head.
Then, place a Water Candle nearby and drink a Battle Potion. Then, all you need to do is run back and forth killing enemies, and you’re bound to get a map eventually.
Once you have the map, you should have a well defended base set up. The base should have lava pits on either side, and any entrances should be blocked off. For the most efficient farm, place actuators over the lava tips and connect them to a lever, which lets you open and close it. If the building isn’t tall enough, you can make a 1 block wide tower on top for the Flying Dutchman to get stuck on.
While you’re inside your base, there’s literally only one enemy you have to watch out for. After killing a pirate captain, his ghost will spawn which can fly through walls and does a ton of damage. Besides that, you can literally sit there and wait for a Flying Dutchman to spawn.
Beating the Flying Dutchman
They can’t actually spawn until the invasion is 50% completed, and when the first one spawns, I recommend closing off the lava pit with actuators. This prevents the event from progressing while you kill the Flying Dutchman.
Probably the best weapon you can use against it is the flying knife, but other weapons such as the Daedalus Stormbow or Yoyos can work well too.
After the pirate ship dies, either open one lava pit or kill a few enemies. When the next ship spawns, close the pit and kill it. All you have to do is repeat this easy grind over and over until you get a Black Spot.
I managed to get 2 in a single invasion, but before that it took me several invasions to get a single mount.