For this trophy, I recommend bringing a diamond/netherite pickaxe of efficiency iii or iv, a shield, a stack of cod (or any other that brings you the medium to high range of decreasing hunger). Also a netherite/diamond sword with the sharpness enchantment and golden apples for emergencies. Armour is also recommended, especially feather falling. If you don't have that enchantment available, bring slime blocks or buckets of water. Wearing other armour is also recommended, one to have at least protection iii.
For unfamiliar players, once you've defeated the ender dragon, go to the end city. Here you will find long purple towers part of the structure - this is where the trophy is based.
Enter the building from the bottom, kill any shulkers with the sharpness sword and make sure your hunger and health is full before continuing upwards.
Go up the first few stairs of slabs, then remove when you're a couple away from the shulkers attacking you. Let them attack you, keep your health up and keep collecting these balls. Once you're in reach of the ceiling, mine out the blocks so you hover out of the building.
Your trophy should pop and on the way down is when you need to use your buckets of water, slime blocks, or whatever you have chosen.
I got mine on the first try.