Shrek, Walter White and Zuko are all amazing characters (and I assume Tony Soprano as well, I'm gonna start The Sopranos after my exams) so I got no issue with any winning but this was a development thread so kinda restricted in regards to what's looked at.
Breaking Bad would probably be at the top for me overall as a story and Shrek is one of my favourite films but I feel like Zuko's development was quite amazing throughout Avatar. From early on, he got comparable focus as Aang with their journies being paralled like in that Storm episode (humanising him and going into why he's so determined to hunt down Aang and how his father permanently scarred him for disrespect, further highlighting his need to reclaim his honour) and we see Zuko change throughout the series from beginning to accept his exile to Azula offering him the opportunity to return back and throw away all his efforts in progressing (signifying how difficult truly changing is especially when actually offered with the opportunity to return back to your old habits) and finally we have him doing his best to atone even when being turned away by everyone he wants to help as a result of his past transgressions. Really amazing and satisfying to see.
All we needed was a 1v1 Agni Kai which we got till certain disruptions which were kinda underwhelming in my opinion but Zuko confronting his father, paving the way for Aang and facing his sister and reuniting with his uncle were all amazing finishing touches to his character arc.
No shame in losing to Zuko. One of the best villain to hero stories out there and Avatar was really well-crafted in many aspects like character-writing and Zuko takes the cake (I think Aang's pretty close but come on, it's Zuko).