The most common and most likely answer to this crossword clue is the 12 plus 10 letter word EXTRASENSORY PERCEPTION
I've seen this crossword clue in The Times
E
X
T
R
A
S
E
N
S
O
R
Y
P
E
R
C
E
P
T
I
O
N
Buddy explains!
The straight part
We know that "The incredible awareness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the incredible awareness = extrasensory perception.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.