Nothing of good value in Grounded is easy to obtain, and this applies to Berry Leather. You can only get Berry Leather from Berries, unsurprisingly, and they can only be found in one location.
Where to find berries
You can find bays on the southeast side of the map, see above. Much like the oak, the Berry Tree is a hive of insects, spiders, and threats. It is advisable not to go to this area unless you really need to. Spiders live all around the base of the tree, so make sure you have a bow, lots of arrows, and armor.
It's also a good idea to set up a Lean-To nearby, set it as the spawn point, and then venture out into the latter part of the journey to try and get the berries. You will be able to see the berries in the tree and shoot them down using arrows, then use your ax to chop them.
Pick up the falling piece of berry, then you need to head to an analyzer. The good news is that there is another field station nearby, indicated on the map above by the purple icon.
Here you can analyze the Berry Chunk, then you will get the Berry Leather recipe, but you will need a Workbench to craft it. Make sure you take as many berries as possible when you are at the Berry Tree, as you want to limit the number of times you have to enter that area. This is one of the affairs of the game when it comes to bugs that want to kill you, and it's best to avoid it when possible.
