The character of Avatar: The Last Airbender all go through remarkable changes and personal story arcs. Prince Zuko's own character arc is among the finest in Western animation, and his uncle Iroh has a remarkable arc as well. Of course, the heroes get their own arcs too, such as Toph Beifong the metalbender and Sokka and Suki starting their relationship.
Toph appeared a few episodes into Book Two: Earth as Aang's earthbending teacher, and she quickly established herself as a true master of all things earthbending. Toph was born blind, so she senses everything and everyone via vibrations in stone and dirt. In many ways, Toph underwent some personal changes, but not everything about her changed so drastically. Some things must remain the same.
10 Changed: Relationship To Parents
Many action heroes suffer from having one or two dead parents. In Avatar, Aang's family is long gone, and Katara and Sokka lost their mother to the Fire Nation. Toph's parents, however, are alive and well — but they don't always get along with her.
At first, Toph bitterly resented her parents for putting her in such a stifling life, but later, she realized that they cared deeply about her and she hurt them by running away. Slowly, she repaired her relationship to them and saw things through their eyes.
9 Same: Seeing Via Vibrations
Toph sees the world by sensing vibrations in the earth through her feet, even stationary objects. She can navigate the land with ease this way, seeing every single rock, hill, tree and more.
She can also sense other people's location and movement if the terrain is correct, and as far as the lore shows, Toph has been doing this all her life and hasn't yet come up with a better method. This style of seeing works so well, she wouldn't even want an alternative.
8 Changed: Avatar Friend
Not many characters in the lore can live long enough or at the right time and place to meet more than one Avatar, but Toph did it. From age 12 through her forties or so, she knew Avatar Aang and some time later she met Korra as well.
Toph thinks that Avatars need an awful lot of "hand-holding," but otherwise, she is rather amused to know two of these famous people, and she got used to Korra being a rather different person than the Airbender Avatar before that.
7 Same: Little Patience For People
As the ultimate earthbender, Toph embodies the patience and stability of the land itself, and this reflects in her personality overall. She takes the long-term view on things and doesn't mind meditating in a swamp for years on end, sensing the landscape changing around her.
However, Toph is much less patient with people, and she often got on Aang's case for being indecisive. She also had little tolerance for Korra's brash and reckless ways. In fact, by her senior years, Toph didn't really like to be around people at all and she barely put up with Korra.
6 Changed: Knowledge Of The Fire Nation
As it turns out, the Fire Nation is largely a very comfortable and prosperous place to live, aside from the conquest-minded Fire Lords who rule it. It's a place of passionate and creative people, and the food, festivals and firebending displays are fantastic.
Living far away in the Earth Kingdom, Toph had no way to know just what the Fire Nation is like, but then she visited with the Gaang in Book Three: Fire and found out for herself. She had fun wandering the land and seeing its sights and wonders.
5 Same: Confidence
Earthbenders are supposed to be firm and unyielding like the stones that they bend, and Toph's confidence is more difficult to shake than an actual mountain. From the very start, she was fully comfortable with her power and her ability to wield it.
Very rarely does Toph show any fear or doubt in combat. Instead, she will firmly take on any challenger, and she usually proves just why she is so confident. Toph is not one of those "all bark and no bite" characters, that's for sure.
4 Changed: Relationship To Katara
When Toph and Katara met, they didn't necessarily get along that well. Katara is group-oriented, while Toph is self-sufficient. She calls it "pulling my own weight," while Katara thought Toph was being unhelpful and self-centered.
They were often at each other's throats, but then Sokka confided in Toph about how much he counted on Katara after their mother died. Toph, in turn, felt bad about running away from her parents and realized how important Katara's mother-figure position was to the group. They got along a little better after that.
3 Same: Loving Pranks
Toph didn't show much of her fun-loving side in her adulthood, but she did consistently enjoy pranks and tricks during the events of Avatar: The Last Airbender. She would sneak off to fight in earthbending arenas and she toyed with Aang when the Gaang visited the Beifong household.
Most of all, it was Toph who started scamming the people of a local Fire Nation town to get a bunch of money, and Katara was troubled by all the antics while Sokka and Aang thought they were fun.
2 Changed: Outfits
Most of the characters undergo a wardrobe change here and there, and Toph went through a number of outfits of her own. At first, she wore her gold and green outfit with a hair band, and in the Fire Nation, she found local versions of those clothes in red, gold and black.
She switched back to her original outfit after that, then she started wearing the distinct metal uniform of Republic City's police. In retirement, she left Republic City behind and went back to her original outfit yet again.
1 Same: Skill At Teaching
Toph learned to bend earth from a pair of badger-moles, the original earthbenders. Ever since Toph mastered the basics from them, she has been the one doing the teaching instead, and she started by hammering the basics of earthbending into Aang.
Toph figured out how to bend metal, then opened her own school to teach other earthbenders how to control metal as well. Some decades later, she helped Korra get her mojo back and remove the last bits of mercury poison from her body.