You didn't embarrass me in the slightest. 你一點也沒有讓我難堪。the slightest是形容詞最高級，在此文法上何解？

應該是in the slightest理解為"是最輕微不過的"意思，文法上是一種"諺語"idioms類別的phrase。通常用作回答"沒有影響到"或"不在意"的加強語氣。

至於翻譯上的用詞要看句中的動詞或所要回應的情況是甚麼，例如這回答句的動詞是embarrass，雖然句中已回答了You didn't embarrass me.這主要答案，附加在後的你可當作是"副詞片語"作為強調"沒有尷尬"的否定程度表示很小很小差不多表示沒有中的沒有。

另一種較為常見而沒這麼造作的回答是You didn't embarrass me at all.都是異曲同功的意思。

Which book are you referring to when you talk about "in the slightest"? You should refer to your recommended book:- TW Chen's the heart of grammar

NO superlative degree explanation.
The idiom:-in the slightest is only used in NEGATIVE
=Not in the slightest
=Not at all
Do I embarrass you?
You do not embarrass me at all
=Not at all
=Not in the slightest
slight--adj.
A slight pain?
=A small in degree
=not considerable to be anything
=Not at all
=not in the slightest.