complete {{the most exercises}} among

Neither really sound right. Adding the number of participants makes the sentence sound stilted. With regard to the correct preposition, I would use "of" rather than "among". So for instance this sounds more natural: "Complete the most exercises of all participants".

The second part "and become a winner" would also sound better if you used "to" rather than "and", giving the full sentence as "Complete the most exercises of all participants to become a winner".

As to reasoning (for disclosure, I am a Scottish English speaker, other dialects may disagree)

1. "Among" gives a sense of choosing a more subjective attribute from a set of possible candidates, and also has a sense of a more fluid definition of the set, e.g.

• "She stood out among her classmates and friends"

  or

• "The most whimsical poem among his works".

"of" by comparison implies that there is a fixed set of possible "winners" which are all being judged based on the same measures. e.g.

• "She came top of her class"
• "It is the longest of his poems"

2. I think "to" gives a better sense of one thing being a result of the other, and is better used when speaking about the future. "and" gives more of a sense of two things happening to occur in succession or parallel, but are equally weighted in terms of importance, and is better used when describing a situation in retrospect. Examples to show the difference:

• "Pass your exams to achieve the scholarship": achieving the first will lead to the second
• "She passed her exams and got the scholarship": this is a list of things she has achieved - there is an implication of cause > effect but it could also just be more of a correlation
• "She passed her exams to get the scholarship": The scholarship was a direct result of her passing her exams, and she put in the effort in order to achieve that goal.

I agree with your hesitancy—it does sound unnatural. If possible, it'd feel more natural to refocus on what entails being a winner, such as:

• "The person in the group who completes the most exercises is the winner."