The most common and most likely answer to this crossword clue is the 12 letter word PHENOMENALLY
I've seen this crossword clue in The Daily Telegraph
P
H
E
N
O
M
E
N
A
L
L
Y
Buddy explains!

The straight part
We know that "Incredibly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case incredibly = phenomenally.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 PHENOMENALLY mean?
PHENOMENALLY adverb- In a manner that is extraordinary or amazing.
- In terms of phenomena.