The most common and most likely answer to this crossword clue is the 8 letter word ABASHING
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result ABASHING
Buddy explains!

The straight part
We know that "embarrassing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case embarrassing = abashing.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does ABASHING mean?
ABASHING verb- To make ashamed; to embarrass; to destroy the self-possession of, as by exciting suddenly a consciousness of guilt, mistake, or inferiority; to disconcert; to discomfit.
- To lose self-possession; to become ashamed.