Hi:
You may have to restart more than “a few times” 
This is a screenshot of Sir William… I’m sure you’ve seen many of these on the internet:
When you kill him, he will drop the rainbow portrait… the portrait is a white item, not a legendary item, so there is no beam of light and it doesn’t show up on the minimap :
You will need to pick it up; in your inventory, the portrait looks like this:
and you’ll need to right-click it to add it to your collection of portraits… where you can select it and equip it.
Good luck in your search !