Here is the question:
What are those definitions of good/bad? Where to find them? How are they built, how did they evolve? How are they reasoned?
This answer will only consider a specific Judeo-Christian perspective of good and bad. Admittedly there may be other, even other Judeo-Christian perspectives, but it offers perhaps a different way of looking at the good-bad dichotomy as a holy-good-bad triple of moral obligation.
The moral law of the Jews requires them to not only be good (clean), as opposed to being bad (unclean). They are moreover obligated to be holy, consecrated rather than common: (Leviticus 20:7)
Consecrate yourselves and be holy, for I am Yahweh your God.
This consecration involves burnt offerings, that is, offerings which did no good, or might even be considered a waste of resources, from a consequentialist, utilitarian, or even virtue ethics perspective. What this suggests is that there is more going on in this moral law than the simple dichotomy between good and bad. Being good (clean, common) is not enough. One is expected to go beyond good and evil, to hint obliquely at an association with Nietzsche as the OP did.
Christians have a similar moral obligation to be "perfect" in Matthew 5:48 although the burnt offerings are no longer needed since Christians believe Jesus was the last such required offering.
This answer is mainly offered to expand the perspective on what is possible with moral obligation in regards to being good rather than bad and to suggest as does G. E. M. Anscombe in "Modern Moral Philosophy" that "moral obligation and moral duty" in terms of the good should be "jettisoned" in favor of some variety of Aristotelian virtue ethics unless one wants to include in that moral obligation the obligation to beyond goodness and to be holy.
Anscombe, G. E. M. (1958). Modern moral philosophy. Philosophy, 33(124), 1-19.
"Leviticus 20:7" retrieved from Bible Gateway https://www.biblegateway.com/passage/?search=Leviticus+20%3A7&version=HCSB