The most common and most likely answer to this crossword clue is the 8 letter word MONGOOSE
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The straight part
We know that "rat-slayer extraordinaire" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rat-slayer extraordinaire = mongoose.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 MONGOOSE mean?
MONGOOSE noun- Any of several species of generalist predatory Carnivores in the family Herpestidae; the various species range in size from rats to large cats. The Indian mongoose is noted as a predator of venomous snakes, though other mongoose species have similar habits.
- Any species of Malagasy mongoose; only distantly related to the Herpestidae, these are members of the family Eupleridae; they resemble mongooses in appearance and habits, but have larger ears and ringed tails.