Sometimes you can upstage the bride by looking better than her, or almost better (viz. Pippa Middleton). And sometimes you can wear something so horribly hideous and distracting that you will blind all the other guests to anything but your strangely monochrome, raccoon-eyed, caduceus-hatted self. Either way, you'll get the attention you so badly crave.
In the funniest coverage of this hat I've found so far, Helen Popkin calls it the Cthulhu hat, saying Bea's choice to wear a "chapeau representing a 'monster of vaguely anthropoid outline' ... really paid off."
P.S. For the record, I loved Princess Eugenie's whole outfit. Sincerely. This is actually what I wear to the Casual Slacks office most days.