The most common and most likely answer to this crossword clue is the 11 letter word MISBEGOTTEN
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The straight part
We know that "Monstrous" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case monstrous = misbegotten.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 MISBEGOTTEN mean?
MISBEGOTTEN verb- To beget wrongly or badly.
- (sometimes derogatory) One born illegitimately (i.e., out of wedlock); a bastard.
- (in the plural) A person born into infelicitous circumstances.
- (of a person) Born out of wedlock; illegitimate.
- (by extension) Ill-conceived.
- (by extension) Bad; worthless.