They are not the same at all.
Credibility means that someone is trustworthy, believable (my definition) from your own link Cambridge says:
the fact that someone can be believed or trusted:
Believing in or trusting someone has nothing to do with them giving a lot of money to a charity.
You might say that someone is credible as a biologist if they have a degree in biology and work in that field... someone who has neither would likely be less credible (less trustworthy).
I don't think you can "gain reputation" (outside of Stack Exchange reputation points)... You have a reputation as something... as a generous benefactor.... or you could generally have a "bad reputation" or a "good reputation" or you can "improve your reputation. Note, reputation can be both positive and negative. If it also becomes known that the person was donating the money only as a publicity stunt, many people may think less of them, giving them a reputation as an attention-seeker. So they might say:
Your reputation [as a kind person who cares about others] will improve because of your generous donation.
If you look at the examples in the Cambridge dictionary, you'll see that none of them involve gaining reputation, only in improving or destroying a reputation or a reputation for something specific ( e.g. being a good doctor).
Also, a change in reputation relates to charity donation only in so much as the fact that the gift is given is publicized. If no one announces the donation in the news or if the charity doesn't tell anyone about it, their reputation is unchanged.
Acclaim usually requires some sort of public recognition... a newspaper has to write about the event and laud the person for their large donation... or someone must have won an award for it such as a Nobel Prize or Academy Award... so, if they know or think that a newspaper is going to write a nice article about the donation, that might work.