Bloodwing
This is also from Borderlands 2. It's not that hard by any means but knowing the history of this character makes this a difficult Boss fight on an emotional level.
All 4 playable characters in the 1st game are NPCs in the second which includes Mordecai and his bird Bloodwing. If you play as Mordecai in #1 you can have Bloodwing fight enemies which makes this twice as heart wrenchingly difficult.
In this game Bloodwing is birdnapped and experimented on by the main antagonist. Sadly he does something to her that causes her to attack you. I don't want to give to much away in case anyone wants to play. Just believe me when I say it will make you feel the feels.
BNK3R (Bunker)
Another honorable mention again from Borderlands 2. This one may not be difficult in an emotional sense but difficult in every other sense of the word.
This twat seems to have hundreds of thousands of HP so it takes a while. He hovers every few minutes of flying around making it a tish difficult to hit him. He also has auto turrets that materializes on his hull as well as mortars, homing rockets and a BFG (thanks Doom). All of which can kill you very quickly if you're not paying attention.
Like all robots he's weakest to corrosive damage so you'd better hope you have a corrosive weapon otherwise this will take a while. And be prepared to die a few times which brings his health back to full, i died twice doing this last night and have almost rage quit in the past. The feeling when you do finally beat him though is awesome so don't give up.