So, I completed all 3 missions of Perils of the Lost Coast on all three difficulty levels but I did not get my feat. When I go to the Completion tab, I have a checked box for Brigandoom! and The Poison Pill, but i have a filled in diamond for Black Fang's Dungeon.

 

I did get my reward card Samisen, but no feat

 

I also bought a character during the legendary difficulty. For him, Brigandoom! is blank, The Poison Pill has a check, and the Black Fang's Dungeon has a filled in diamond.

 

Question 1:

How do I read this completion tab? What's the difference between blank, checked, and diamond? Also are there any other symbols?

 

Question 2:

How come I didn't get my feat?

 

Question 1:  Check means you have completed the Scenario on any one difficulty.  Blank means you haven't yet completed the scenario on any difficulty.  Filled diamond is actually OVER the checkbox to indicate that this is the Scenario you attempted most recently.

 

Question 2:  You only ever get a Scenario or Adventure reward ONCE, no matter which difficulty you completed it on.  So if you got the feat when you did it on Normal difficulty, you won't get it on Heroic or Legendary (or repeating Normal).

Also, you may be confusing party progress for character progress. Have you completed all three with a single character? In general, until you're comfortable with the game, don't change your party.