I found published results of my mentor to be wrong. How to tell her?

As a matter of fact, I believe there is no such thing as guilt or ruin for other people's work when it comes to the academic aspect of the knowledge. Actually, if you do not share this with your mentor in order to be fixed, you may ruin many other further research...

I suggest you do this respectfully and carefully. You can go to your mentor and talk about this problem. You can show her your code and your understanding from the paper, then confirm whether or not you are right. Let her decide what she can do about this. There is also a slight chance you have made a technical mistake while investigating their work, so keep this in mind when you discuss the issue.

I suggest you treat this as a learning process. After all, you have spent on this only a week, while the authors have spent significantly more, so there is a chance you are wrong.

So, with this working theory in mind, present your results to your mentor and discuss with her what you think is wrong with their work and why and ask her to explain what you could be missing.

After the discussion you should, ideally, either realise why you were wrong; convince them of what they did wrong; or all of you agree to disagree on the correctness of the results. In the second and third scenario, your mentor should be able to suggest some path.

I do not think you should be asking them to retract the paper unless they have shown gross negligence in the research process or outright cheated; it should be up to them.

I think there is a simple answer. From what you wrote it sounds like you rather "could not reproduce the results" than "proved that the results are wrong". While the first is often an indication for the second, this need not be the case (especially since you "rewrote the entire code").

Now focus on a solution instead of the problem. What you should do is: Approach your mentor with "I tried to reproduce the findings of the paper in this and that way and ended up with different conclusions." From there on the story may evolve differently: It may be that there is a misunderstanding about the "missed obvious things", it may still be bugs in your code, it may that the paper was ambiguous about some things, also it may be that there is something wrong...

In this discussion be sure to be open minded and free of prejudice. As an example: When somebody tells me something in a scientific discussion that I think is wrong or bogus, I get a much better and helpful response when I say "Sorry, I did not understand that, can you say it differently?" than "That's nonsense."