The first letters of one wave (the one beginning with Oliver Purpletooth) spell ORDER. Let's say this is the first wave, and look at the second letters of some other wave (the second wave), and so on. With the words extracted in the right order, we get the message ORDER WIELDERS BY WEAPON LENGTH.
Six pirates have weapons in their names. I don't know how long any of these weapons are in physical space, but we can order them by word length easily: AXE, DART, SABER, MUSKET, CUTLASS, BLUNDERBUSS. So we order those pirates thusly:
The first letters of their names spell the answer, RAGING.