Balancing a fighting game is one of the hardest things to do for a developer. They have to take into account how strong a character is in the game's lore, how new players will perceive the character, and the legacy of the character from games past. Juggling all of these pins sometimes leads to mistakes in balancing.
Broken characters can be way too strong, or way too weak. The overall question people should ask is "do they work in the context of the game?" This question usually helps determine if a character is broken or not because weak ones generally don't have enough options in common situations and strong ones have too many options, or their options can just end the game then and there. SoulCalibur games have been in a tug of war between overpowered and underpowered since the franchise's second installment.
Hilde - SoulCalibur IV: Overpowered
Hilde was introduced in SoulCalibur IV as a character with fresh mechanics to revitalize the way players enjoyed the game. Her special ability was to charge certain moves and unleash them in devastating combos for a lot of screen space and damage. The issue with Hilde was more of an issue with SoulCalibur itself.
The game would allow players to charge multiple moves and then chain them together with minimal effort due to the way button bindings worked. This lead to Hilde players escorting their opponents out of the arena from round-start any time they got a hit. She was banned from competitive play in SCIV for this very reason.
Tira - Soul Calibur III: Underpowered
Tira was introduced in SoulCalibur III as a unique character with a quirky weapon and special battle mechanics that no other character had. The hype for Tira was all over and fans couldn't wait to get their hands on the character. After the release, fans were pretty disappointed because Tira just didn't seem to work. The developers left out her special mechanic because they couldn't implement it properly and saved it for SoulCalibur IV.
In SCIV, Tira returned with her special mechanic: two modes she could switch between called "Jolly" and "Gloomy" which affected her moves and damage. Again, fans were disappointed because the modes didn't add much in terms of gameplay, and Tira herself was actually quite weak. It wasn't until SCV that Tira felt like a fully realized character.
Yoda - SoulCalibur IV: Overpowered
Yoda in SoulCalibur IV is a poster boy for broken characters in any genre of competitive game. To start off, his character model was too small to actually get hit by a lot of moves from other characters. SoulCalibur relies on movement and reading the opponent's movement on the battlefield. Even if players could get a read on Yoda, they had to change their whole approach to stopping him since he could duck under attacks.
Yoda was considered broken because he also had higher mobility than normal, which made him even harder to pin down. His damage output was nothing crazy, but it didn't need to be since so many players couldn't hit him.
Z.W.E.I.- SoulCalibur V: Underpowered
Z.W.E.I. was another unique character added to SoulCalibur V who could control a minion during battle to extend combos and set up pressure. The concept on paper was fantastic but executing it proved difficult for the developers. It's easy to introduce something new and make it too strong, so to balance Z.W.E.I., the developers gave him short-range and a cool down on his minion.
These balances went a little too far in weakening Z.W.E.I. and he had to work really hard to get his game plan in motion. Players with high mobility were also able to punish him for a lot of his set-ups if they guessed right, meaning it was more dangerous for the Z.W.E.I. player in some situations.
Xianghua - SoulCalibur II: Overpowered
Xianghua in SoulCalibur II was a menace to new and veteran players alike. Her move set was generally the same as it is today, but it hadn't been tweaked over time to become as fair as it is now. Xianghua had the ability to fake out her opponents, feinting certain moves while actually hitting her opponents with a different move.
On top of these feints, Xianghua also had spammable moves that were safe on block and hard to deal with. The opponent's best bet to stop them was to move around the attacks and punish from a different angle, but that's not always what's on a new player's mind.
Leixia - SoulCalibur V: Underpowered
As a direct contrast to her mother Xianghua, Leixia was introduced to put a fresh spin on the character archetype. The biggest issue with this approach was that she didn't have anything that made Xianghua really strong. Leixia was supposed to be a mix up heavy character that could pressure her opponents by making them guess how she would approach but all of her approaches were slow and telegraphed.
Leixia also didn't have the Silent Xi Sheng Stance that made her mother such a menace in SoulCalibur IV. It was clear that the developers didn't want a repeat of SoulCalibur II, but they took some things too far in the other direction and made a character that not many would want to play if they knew what was possible in games prior.
Viola - SoulCalibur V: Overpowered
Viola was a step forward in a new direction for the SoulCalibur series, trying out new weapons and unconventional mechanics to make the game more interesting. Viola used a floating orb to pressure her opponent, unlike the bladed weapons the rest of the cast used at the time. Mastering Viola was extremely difficult and took a lot of time because her combos were very precise.
On the release of SoulCalibur V, players actually petitioned to have Viola banned from tournaments because of her great spacing capability and insane damage potential. After a few weeks of practice, players found that she could kill opponents from full health, and that she had multiple infinite combos. These are grounds for bans and changes but the community never fully agreed on how to approach the Viola issue.
Dampierre - SoulCalibur Broken Destiny: Underpowered
Dampierre's whole design was built around being a character that could surprise his opponents with his tricks and antics as a joke character. Generally joke characters aren't the best characters but there're ways to balance them to make them at least fun to play. Dampierre's weird mechanics and short range made him a joke of a joke that no player wanted to touch after seeing what he could do. All his opponents needed to do to counter him was wait and see how he would approach. He was very predictable and couldn't control the pace of a match himself. Even if he did land a hit, it never hurt much so the threat was low.
Ivy - SoulCalibur II: Overpowered
Another goddess from SoulCalibur II, Ivy was one of the strongest characters to ever appear in a SoulCalibur game. For starters, her damage off regular combos was unreal since her normal combo starter was so powerful. When players could convert that kind of damage off stray hits, it really adds up until the opponent is defeated.
Secondly, the thing that really made her powerful was how easily she could buffer specials behind her attacks. Her Calamity Symphony and Summon Suffering were easy to hide behind normal attacks to trick opponents. There was also a glitch that made it a true mix-up between her strike attacks and command grabs, so opponents were always guessing versus Ivy.
Kilik - SoulCalibur V: Underpowered
Kilik has been a staple to the SoulCalibur series since the first entry. Over every game he incorporated his unique style and it developed each time. In SoulCalibur IV, Kilik players had options for dealing with opponents from long and close range, making him a versatile and fun character.
When he was included in SoulCalibur V, they took away everything that made him fun and homogenized him to play more like the rest of the male cast. Not only did they take away his best tools, they even weakened his more normalized moves, making him a seemingly useless character. At that point, the only reason to play Kilik was for character loyalty, not to play a fun and unique playstyle.