Now in this guide i'm gonna tell you most of the ways you can get discovery points.
When you reach 51 you need discovery points if you want to advance more in level. Luckily there is some ways to achieve more dp.
Make yourself a ship. Then you just sail out to different kind of islands to get dp. Most of the islands you discover will give you 2 points. But in some islands it is also secret discoveries. They will give you alot more dp than the island discoveries do. So be sure to take some time to look around the islands for them!
Okay so the next method is alot harder since you are gonna do powerstones. Each time you finish a powerstone you get alot of dp. But in order to do that you must first defeat the boss. This will either be Hydra or Drake. By sailing around the island you will find the Hydra idle. Once you found him he will go after you and you need to prepare yourself. If he gets too close your ship is doomed. Hold distance from it and shoot and shoot. Ballista is one of the best weapons against the Hydra. One of the best methods to kill the Hydra. So i recommend using it. I do also recommend to bring ALOT of ballista shots or cannon balls or whatever you wanna use. Because a Hydra has alot of health. The Hydra has three heads you must defeat so take note of that. The best method to killing the Drake is to hide around the island where he can't get to you and keep firing arrows, or just use your cannons and ballista on ship. Shooting arrows take so much longer than cannons and ballista so i would kill them with ballistas. Once you defeated the boss you will get the artifiact key. Now you have to run inside the powerstone place and get to the powerstone thingy and press e on it to get the powerstone. Be aware because there is ALOT of enemies there. Keep doing powerstones and your level cap will increase so much! If your one or two i recommend to bring npc with you so they can man the ballistas, cannons to kill it faster. One of the powerstones you need (cyan) you must defeat the Ghost Ship to achieve it.
This method is much more easier. What you will do in this method is to spawn on all different kinds of freeports. Once you spawned in a freeport make a raft or sloop and sail out to all the lawless, normal islands in the area. Use the link i told you above to find the secret discoveries faster. The game has been updated alot so more discoveries have been added. So not all of the discoveries may be listed in the wiki. Be sure to check every place in the islands anyways. Once you have collected as many discoveries as possible in the islands you can teleport to the next freeport, and repeat. By doing this you will get a ton of points. I also recommend to spend points in the harvesting skill so you can gather resourcers fast to build your ship. Also many secret discoveries can be placed in places where you need a climbing pick. Be sure to have "Advanced Tools" unlocked. So you can make some. If you try to look around the island there is usally smithies that people have put down. So you don't need to make one and spend time on that. By the way if you don't know how to teleport to new freeports just click on "change home region" and you pick one from the list.
The 4th method on achieving discoveries is to defeat whales. Here it is most efficient to have a schooner with ballistas on the back. Ballistas is very efficient against whales. There is Blue Sperm Whale and Mean whale. Both types of whales will give quite alot of discovery points. Remember to not let them hit your ship! There is also quests to kill the Sperm whale and the Mean Whale. So not only discoveries will you earn but also +30% taming affinity boost by killing the Sperm Whale, +100% prone speed and +50% crouch speed by killing the Mean Whale!
Two Quick Tips and the End
This is all of the methods i know in getting discoveries. Now im just gonna tell you two quick tips. If you use a spyglass you can discover some islands without having to sail your ship and going on land. But this may not always work on all islands. Remember to always have with you climbing picks or grapple hook since some discoveries can be in unreachable places, i highly recommend it.