Be willing to throw lots of seeds at the event, as well as clicking on Raid Boss in the menu over and over again to refresh the list.
Oh, and having the luck to actually pull at least... 1? copy of an eidolon from the event gacha to actually 4* it. At least, in the version of the raid system up to this point. I believe that starting with the next raid event, the reward format got updated such that sheer large quantities of time and BP thrown at the event should be sufficient to max the eidolon/weapons.