The Lords of the Fallen boss weapons are a lot easier to get than in most of the other Soulslike games you might have played. Usually, you defeat a boss and get an item that you can trade for a single weapon or spell of your choice, but in Lords of the Fallen, you can pick and choose what you want to purchase with Umbral Scourings.
Essentially, when you defeat a main boss, a memory will appear in their arena that you can Soulflay using the Umbral Lamp. This will give you a remembrance for that boss, allowing you to purchase its equipment once you've unlocked the ability to buy boss weapons with a specific vendor.
Here, I'll explain how to get boss weapons in Lords of the Fallen, plus the best way to gather the Umbral Scourings you need to buy them.
How to get boss weapons
To buy boss weapons, you first need to grab the Bowl of Revelations item in the umbral version of the Pilgrim's Perch area. This is after you unlock the Vestige of Blind Agatha rest point in the Bellroom. From the vestige, head right down the tunnel, past the enemies, until you reach a big open area with hanging crosses, and a suspended platform that's slowly rotating.
If you switch to the Umbral here and look down, you'll see a much lower platform with lots of petrified winged enemies standing up around a corpse. Follow the walkway going right, watching out for the spike-headed enemy at the far end, take the ladders all the way down to the platform, then use Soulflay on the corpse at the centre with your lamp to get the item.
Now you've got the bowl, you can take it to Molhu in the umbral version of Skyrest Bridge. If you haven't found him yet, simply switch to the Umbral by the vestige, then head up the stairs near Pieta. Give him the bowl and you'll unlock the ability to purchase boss weapons, spells, and armour using Umbral Scourings.
To get a specific boss's equipment, you need to have the defeated boss's remembrance, so don't forget to Soulflay the memory in their arena after the fight is done.
How to get Umbral Scourings
The main way to get Umbral Scourings is by defeating bosses in the game, but it's worth noting you can also obtain them by using Soulflay on memories with the lamp in the umbral realm. Whenever you defeat a main boss, a memory will appear in their arena, granting you both their remembrance and some scourings when you Soulflay them.
There are, however, other memories scattered throughout the umbral realm and in secret areas that will give you story items and extra scourings to buy boss stuff—these are pretty easy to recognise, since they kind of look like ghosts or ethereal figures standing in place. Simply target them and use Soulflay to play each memory. Once the sequence is concluded, you'll get your scourings.