For all those saps that can't make a decent OC, here are some tips to NOT make a Mary Sue.

*She has to have a name of Asian background. Like my character's name is Vayu, the Hindu god of wind. Ursa, though Latin, isn't a common name for girls and means "bear" referring to Ursa's protective nature of Zuko. No Jennifers or anything.

*She has to look like the nation that she's from. Your character can't have blonde or red hair, and especially no highlights. If it hasn't happened in the show, you cannot do it. And no changing eyecolors.

WT girls have dark brown hair, blue eyes, and tan skin. Yue is an exeption to this.
EK girls have black, brown, or dark brown hair. Green or brown eyes, and light or tanned skin. Your girl has to have her hair in a braid or something that EK girls wear. Men's hair are in topknots.
FN girls have black or dark brown hair, gold/amber or dark gray/silver eyes, and pale or fair skin. Commoners wear red and white clothes, nobles and politicians wear black and red. Girls and boys wear topknots.
AN girls have dark chocolate brown hair, dark gray eyes, and fair skin. Boys must be shaved.

*Clothes, your girl must wear the clothes of her nation.

WT girls wear blue and white fur jackets, dark gray pants, and dark gray shoes. Only 16 and over girls can wear betrothal necklaces. Since Katara already wears her dead mother's betrothal necklace in her memory, your girl can't since its already been done.
EK girls wear multiple colors, but green and brown are most common. They can wear purple and pink, even blue, but no red and black combined. Or even seperate.
FN girls wear red and white if commoners and red and black if they are noble or are politicians. Only official nobles and politicians can wear the two pronged flame topknot piece. If related to nobles or are nobles kids, your character can wear the topknot piece.
All Airbenders wear orange and yellow Airbending clothes that differ depending on where their from.

*Her past. If she's lost a parent, then have her be sad, but not depressed even years afterward, all the time, about it. Since its Avatar on Nick, she can't have been raped or abused, then again, it is your fic, but still.

If from the WT and she's grown up in the North Pole, she has to know how to cook, clean, and other such duties. If a female Waterbender, she can heal, but she can't fight. The girls of the North Pole don't know their rights and therefore wouldn't know how unfair it is that they can't fight.
The Avatar world is basically ruled by guys, girls can't or aren't allowed to fight. Unless your girl is outgoing, she won't want to fight. Since the EK is largely involved in the war and is not male dominant, she can have just about any past you like.
If from the FN, she is raised and brainwashed to hate the EK and support the war. She can be like Ursa and not like the war because it has killed her family, but she still supports it.
I won't go into AN.

*Personality. I find that all Mary Sues are angry, hot tempered, bossy, and rude. So try and avoid that in your character.

WT girls are calm, friendly, and don't know their rights, being ruled by men and made to believe that they have to obey them.
EK girls can be tough and headstrong. But friendly.
FN girls can be pleasant and nice, or angry and spiteful.
AN girls can cheerful and friendly.

*Powers and Skills. Your character can be skilled like Katara and Azula, but don't overdue it.

    Waterbending girls are taught how to heal, and since the girls are brainwashed, she cannot want to fight.
    Earthbending girls can be about any rank.
    Firebending girls, I can't say, because we've only seen one (Azula).
    Airbending girls come from the Eastern or Western Temples, they have just as much power as men.

If they are benders, then don't give them additional skills. Zuko is a different story. If she's not a bender, then give her a unique weapon and make her good at it. She can't have any other skills. Ty Lee's acrobatics link to her skill in pressure points.
She can't be a telepath or anything else. Only bending is allowed.