The strongest woman on set of the game of thrones is Yara Greyjoy, although lady Brienne comes close to the title, yara has never displayed weakness, either emotionally nor physically. She can stand up to any man or beast and take it for its own. This is why Yara is also chosen as the leader of the iron islands.
Yara Greyjoy has proved along her reign that she does not flinch when it comes to her closest ones dying or betraying her. He is a strong independent leader who is fearless and ready to tackle anything that comes in her way.
In my opinion when it comes to who the strongest woman is in the Game of Thrones series I would have to say that distinction would be given to Yara Greyjoy. Yara is the embodiment of what a strong and tough woman would be and look like when it comes to the world of Hollywood. While a lot of the ladies on Game of Thrones are sexy and sultry, Yara Greyjoy looks like a woman that could hold her own against any mightly warrior male.
Yara is the first openly LGBT charchter in Game of Thrones and she is able to play the masculine part to a hilt on screen. Yara is certainly the toughest female charchter on Game of Thrones. There are men who shake at the knees at the sight of her and there are certainly plenty of women in the series who have no kind of interaction knowing that they are talking to someone who is more dominant than they are.
I will go out and say without a doubt that Yara Greyjoy is the strongest woman on Game of Thrones. There could some kind of argument for ladies such as Stansa Stark, Margery Tyrell, or Cersei Lannister, but in my opinion the strongest lady on Game of Thrones is Yara Lovejoy.