The most common and most likely answer to this crossword clue is the 5 plus 7 letter word GROUP THERAPY
I've seen this crossword clue in The Guardian
G
R
O
U
P
T
H
E
R
A
P
Y
More clues leading to the result GROUP THERAPY
Buddy explains!
The straight part
We know that "How to get over the Beatles breaking up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case how to get over the beatles breaking up = group therapy.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.