The most common and most likely answer to this crossword clue is the 8 letter word ZIGZAGGY
I've seen this crossword clue in The Times
Z
I
G
Z
A
G
G
Y
Buddy explains!
The straight part
We know that "Serpentine" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case serpentine = zigzaggy.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.