Translation:She wants to win by any means necessary.
The equivalent English sentence would be "she wants to win by any means," meaning she wants to win no matter what the cost. "By all means" in English means "of course" or "certainly," like what you're saying should be obvious. So, if you were going to make a sentence out of it, it would require a comma: She wants to win, of course.
The thing is: "by any means" says that you are ready to use every and each possibility that you see to reach your target. Still following me, now comes the hard part: "mit allen Mitteln" means that you use all that you have to reach your target. So the difference is that in the first clause you are definitely going to do whatever is necessary while the second clause means that you use from the start all that is possible. There is also a difference in determination to see here. "any means" is somehow emotionally stronger than "all means" because it implies that you will do the unknown while "all" just means "all". No more and no less. Also keep in mind that you are asked to translate as precise as possible and "by any means" is "mit jedem Mittel" in German.
I hope I could be of help.
"By all means" in English does not always mean "of course" or "certainly as in the situation:
"May I have a glass of your wine?" "By all means."
Still, I think ToyJazzer is right in saying the translation is poor. It should be "she wants to win by any means necessary." More difficult German is not needed to reflect this. Often, as this situation demonstrates, direct word-for-word translation is not correct or needed.
In trying to translate from German to English, I think we have to wrestle here with both cultural and linguistic differences. Neither "She wants to win by all means" nor "She wants to win by any means" captures the meaning of the German sentence.
Imagine playing the telephone game. You whisper the German sentence in someone's ear. They then whisper an English translation in the next person's ear. That person then whispers a German translation of what they heard in yet another person's ear. And so forth down the line. What are we likely to get?
Sie will mit allen Mitteln gewinnen. → She wants to win by all means. → Sie will auf alle Fälle gewinnen. → She wants to win in any case. → Sie will auf jeden Fall gewinnen. → She definitely wants to win. → Sie will unbedingt gewinnen. → She wants to win. → Sie möchte gewinnen. → She wants to win.
But suppose we translate Sie will mit allen Metteln gewinnen as "She wants to win by all means necessary" (as suggested by person243). Then the game goes like this:
Sie will mit allen Mitteln gewinnen. → She want to win by all means necessary. → Sie will mit allen Mitteln gewinnen.
This strongly suggests that "She wants to win by all means necessary" is a better translation of Sie will mit allen Mitteln gewinnen than simply "She wants to win by all means."
The problem for Duo is that German-learners are not going to think of adding "necessary" to the English translation. If that's what's needed for an accurate translation from the German to English and back to German, why isn't it there in the original German? Perhaps that's because it's not needed in the German, because it's already understood in the German culture. But in the English-speaking world it needs to be made explicit.
Duo may not want to change mit allen Mitteln to mit allen nötigen Mitteln because that's not how it would be said in German, and Duo certainly wouldn't want to surprise us by simply adding "necessary" to the end of the English translation "She wants to win by all means," because German-learners would see that as coming out of nowhere. But Duo could change the drop-down hint for mit allen Mitteln to "by all necessary means." Not everyone looks at the hints, but this would make the hint more accurate and lead to a much better English translation, which could be seen as justified or properly prepared.
As noted above, then the game goes back and forth between Sie will mit allen Mitteln gewinnen and "She wants to win by all means necessary."
NOTE: How does anyone know how the telephone game will go? They don't really. But not having a dozen people available, I played it on my own by asking Google to translate at each step until the chain stabilized. I thought the results might be indicative and helpful.
Having read through this page, I think there's a chance we're over analysing this. The point of the exercise is about giving rough parity between a German idiom and an English one. Idioms don't stand too much grammatical analysis. They are an "off the shelf" linguistic device to convey the gist of an idea that both the speaker and the listener recognise without dissection.
I would summarise the long discussion about the inclusion of the word "necessary/nötig" by noting that in both the English and the German, they are implied even if omitted.
The goal in translation is always to express as closely as possible the same idea in another language. If the expression to be translated is an idiom, the goal does not become to find the idiom in the target language that's the closest, but remains to find the closest translation regardless of whether it's an idiom in the target language. Of course, if an idiom in the target language satisfies this requirement, that's great!
The claim that the idea of "necessary/nötig" is implied in both the German and the English, even if omitted, is a correct statement about the German sentence here and Duolingo's English translation, but requires clarification. The point is that it is culturally implied in the German sentence, though omitted, but needs to be explicitly added to the English translation, in which it would not be implied simply by the culture. This is the amount of analysis needed—neither too much nor too little—to understand the otherwise surprising appearance of the word "necessary" in the English translation.