I think the reason Sonya Blade gets mischaracterized so often is how little her solo story was actually covered. She has had so many different aspirations and goals throughout the series that it’s easy to lose track of what she really wanted.
Besides the obvious "protect Earthrealm" duty, Sonya has several other motives driving her presence in the games and media. I will try to break down some of her core character traits:
Sonya's first motivation:
Her enmity with Kano. In the original Malibu comics it was stated that Kano killed her fiancé, so now she is eager to get revenge. In alternative universe (MK9), Sonya tells Johnny that Kano was their informant in SF and he betrayed her, resulting in death of SF troops.
Both of those reason behind her desire to revenge is getting betrayed. I like to think Sonya was likely already a guarded person, but these event caused her to become truly distrustful. She lost her faith\trust in informants (outside help), which is why Sonya was so hostile toward Johnny's offers to help her at the start of MK9 (not even mentioning his annoying pickup lines).
Armageddon: "For a long time my objective was to hunt down and eliminate the rogue clans of the criminal underworld. Kano, a member of the Black Dragon, had been a particular thorn in my side. I was close to capturing him, but once I heard about Shang Tsung's Mortal Kombat tournament, protecting Earthrealm from invasion became my sole priority.
Sonya's second motivation:
"As a girl, Sonya idolized her father, a U.S. Marine. When he embarked on a covert operation and never returned, she vowed to honor his memory. She joined the Marines and pushed herself hard, quickly rising in rank. Sonya's impulsiveness didn't win her many friends, but her skills and loyalty gained the respect and admiration of all who fought beside her. Though she has never given up her quest to uncover the truth behind her father's disappearance, she realizes that she might never see him again. Now Sonya finds herself caught up in the mysterious Mortal Kombat tournament. Like her father, she too could become a casualty of war."
It is known she had a father, who played a big career-choosing role for her. But we never hear anything further about him or Sonya's thoughts. After completing her tower in MK9, we see her driving on her motorcycle (cool girl cliche, but still really cool). When I first looked at the picture, I thought the ghost was Jax. Wouldn't that be more logical after the ending of MK9 story? idk. Nevertheless, it was her missing father Herman, haunting her.
Honestly, I cannot distinguish what that plot brings to her character, except for it being a reason why Sonya decided to be soldier. And that she has a motorcycle. A far-fetched guess would be that Sonya likes motorcycle because she is a headstrong and emancipated woman.
Sonya's third motivation:
Helping Jax. This one has been used in MK Legends: Scorpion's revenge. She came all the way from USA to Shang Tsung's island to rescue her C.O. and her only close friend. The way she is doing that alone is supported by idea that she doesn't want to be abandoned again (like with her father's disappearance). I'm not saying that Jax was Sonya's parent figure, but more as a protective one. It is known that Sonya is impulsive and fights right away, instead of thinking first. So, Jax was her grounding presence.
Overall, people mostly mischaracterize her because of a lack of coverage of her solo story without rescuing Jax (or vice-versa) and fighting with Johnny.
Also, she has a sense of humor for sure. Sonya is bold and confident, she just doesn't boast about herself.