"O candidato pode ter mais experiência do que é normal e contar com a maior parte ou todas as habilidades relevantes para o trabalho"

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“The candidate may have extensive [work] experience and, in addition, have all or most of the key skills for the position.”

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There are a number of acceptable variations of this. I think that the important thing is that you don’t have to use “above-average” or “greater than normal” or the like in the translation. In fact, I think that the original would have been better had it reflected my suggestion for the English translation (because what, in the end, is to be defined as “normal”?).

I am guessing that the larger context here reveals that the intention is to indicate that greater experience can substitute for particular formal requirements (i.e., a specific college degree or certification). “Extensive experience” or “extensive work experience” seems to accurately convey the intention of the Portuguese here.