My son is the poster child for strong willed children. I remember him first testing me when he was 9 months old. He could not walk but had climbed on a chair and was swinging some pictures that were hanging on a wall. I picked him up, said "no, no" while pointing at the picture, and put him down on the floor a little ways away. He went back there, climbed back up on the chair, and did it again. I again told him no and put him back down on the floor. So he climbed back up, looked at me sideways, and while still looking at me out of the side of his eyes, reached his hand over and swung the picture again. At 18 months, he started hitting when he did not like something we said or did. For two months, it was daily, several times a day having to deal with that. Then he switched it off one day, and the next day started biting. Two months of that. Then he switched that off, and started the very next day making himself throw up. If he asked for a cookie and we said no, he would stick his fingers way in the back of his throat and would make himself throw up. At first, we thought he was just sick, but after a few days of this happening multiple times per day, we realized he had somehow figured out his throwing up really made us concerned/disturbed, so he was using it as a power play. It is amazing how a kid even at that age can really push the boundaries in the most creative ways.
I read a book called "The Strong Willed Child", and it had a lot of examples about things that strong willed children did, but I kept thinking those kids were pansies compared with my boy. For every example the book had, I had three more, and 10 times worse. Fast forward to 14 years later. My boy is still strong-willed, but he has learned to choose how to use that strength, which issues are important enough to set his foot down on. He told me recently I was his best friend, and it does not surprise me, since he is mine. He makes straight A's and is being courted by MIT and Caltech. He, like his sisters, treats my wife and I and other adults with respect. We still see the strength of will, but applied in ways that are awesome to behold.
I don't know that there is one single thing that helps one deal with such a kid and train them properly. It is everything that we do. But I would say there are several areas that are important.
First, the messages we give to any kid, as parents must be: 1) I love you and I will always love you, no matter what. 2) You are awesome. 3) If you do wrong, it will meet with loving, strict, firm discipline. 4) if you do good, we will celebrate with you. Those messages are indispensable to a child. They must know where the boundaries are - that is why they test. And on a bedrock of love and appreciation, those boundaries will be a joy to the child, and the discipline will not be disheartening to them in the long run.
Part of this also has to do with training the child to know what is wrong and what is right. One basic principle that we have strongly pushed on our kids is the idea of doing to others as you would have them do to you - or love others as you love yourself. Fussing and demanding from parents is disrespectful, unloving behavior and is wrong. That cannot be tolerated, for the sake of the child.
One last thing on discipline. Discipline must first and foremost be about training the child. It will have an element of punishment for wrong-doing, but good discipline is not mainly about punishing. It is about training and teaching and reinforcing what is right and what is wrong. Discipline should never be a vehicle for parents to vent anger at what the child did, so when we get angry, we need to take a step back and wait until we can discipline with a cool head. And discipline should never happen for something that is a mistake, accident or something the child did not know. Spilt milk, accidentally knocking mom's favorite vase off the table and breaking it - these should not be reason for discipline. But once having been told something (ex: don't touch mom's vase), if the child then does it, then they are disobeying and that is wrong and should be met with discipline.
And one thing on strength of will. As I was thinking further on this, I wondered if other parents with strong-willed children have a lot more trouble than I did because they are less strong-willed than their child. I happen to be an extremely stubborn person (like father, like son). And this served me well with my son. He needed to learn that he would not just get his way by fussing or acting up until he wore me down. I am too stubborn to be worn down like that. Less stubborn parents may have to stretch themselves into levels of being firm that they are not naturally comfortable with. But be careful, it must be gentle firmness, not harsh stubbornness, or else you could turn your relationship with your child into an antagonistic mess. The child must understand that you can be absolutely firm, for a good reason (explain it), and will be so as kindly and gently as is possible.
Love your child and rejoice in the strength of her will. This is not a bad thing. There are hills worth dying on (I hope you know that English expression), and it is the strong of will who will hold those hills. It is a matter of teaching a child what is worth fighting for and what is not. They need to know what is right and what is wrong, and what is neither - plenty of things where we have freedom to choose - and how to tell the difference in a principled way.
My prayers for you and your family - this kid of yours has awesome potential!