The most common and most likely answer to this crossword clue is the 8 letter word CAPTIOUS
I've seen this crossword clue in The Times
C
A
P
T
I
O
U
S
More clues leading to the result CAPTIOUS
Buddy explains!

The straight part
We know that "critical" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case critical = captious.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 CAPTIOUS mean?
CAPTIOUS adjective- That captures; especially, (of an argument, words etc.) designed to capture or entrap in misleading arguments; sophistical.
- Having a disposition to find fault unreasonably or to raise petty objections; cavilling, nitpicky.