The most common and most likely answer to this crossword clue is the 4 letter word FAUN
I've seen this crossword clue in The Daily Telegraph
F
A
U
N
Buddy explains!
The straight part
We know that "character of godlike nature" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case character of godlike nature = faun.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 FAUN mean?
FAUN noun- A woodland creature with pointed ears, legs, and short horns of a goat and a fondness for unrestrained revelry.
- Any of various nymphalid butterflies of the genus Faunis.