The most common and most likely answer to this crossword clue is the 13 letter word MAGNIFICATION
I've seen this crossword clue in The Times
M
A
G
N
I
F
I
C
A
T
I
O
N
Buddy explains!

The straight part
We know that "blowing things up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case blowing things up = magnification.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 MAGNIFICATION mean?
MAGNIFICATION noun- The act of magnifying; enlargement; exaggeration.
- The apparent enlargement of an object in an image.