「日本一の嫌われ者」って英語でなんて言うの？

An all time low - An all-time high, low, best, etc. is the highest, lowest, best, etc. level that has ever been:
"After three years of drought, the water in the lake had reached an all-time low."
To loathe - feel intense dislike or disgust for.
"She loathed him on sight"

A. Do you know that celebrity?
B. Yes, of course, everyone knows her -- she is notorious and known for all the bad reasons.
A. I know, here in Japan, the public despises her.

To express very strongly how hated she is, you could say that she is “the most hated”.
If you do not mean it as strongly, you could say that “nobody likes her”.

Native speakers will say like this: “She is despised by Japanese residents”.
There are lots of other ways to say it, but this one is the most accurate and most commonly used.
Here is an example on how to use this in a conversation:
A: I can't stand the new Japanese politician.
B: Yes, everyone in Japan hates her.

The three sentences you see provided above are great ways to express to your listener that a particular person is the most hated person in Japan. In the second sentence you will see the word despise and in the third sentence you will see the word loathe. Both of these words mean hate. These words are appropriate for both formal and informal settings.

"She is probably the most hated person in the whole country." is a way to tell someone that the person you are talking about is very much disliked by almost everyone in Japan at the moment. The word "despise" means hated intensely and used in a very strong way.

To say that someone is not very popular or hated by the Japanese then you could simply say 'She is hated by the Japanese/Japanese people'
If you want to explain thats she is hated at this time then you could add 'right now' or 'at the moment' meaning at this present time