When Phantoms were added in the 1.13, they also brought with them a new item drop: Phantom Membrane. These gross-looking items can be used to either repair Elytra at an anvil or combine with an awkward potion to brew a slow-falling potion. Either one can be pretty useful, so you’ll want to know how to get your hands on a Phantom Membrane. There are two ways that you can get some, and while neither are a guarantee every time, the odds aren’t bad at all.
Kill a phantom
A simple solution. These flying enemies will come out when a player has not slept for three or more in-game days. You can kill them with your own weapon or a tamed wolf. Phantoms can drop anywhere from zero to two phantom membranes when killed, and if you add to that with Looting, you can get that maximum up to 5 at Looting III.
Get a cat
While not incredibly likely, sometimes a tamed cat will be able to catch a Phantom and bring you back its membrane. The odds of this happening, however, are only 3.22%, so don’t believe that it is a sure thing.