The most common and most likely answer to this crossword clue is the 7 plus 7 letter word PITCHED BATTLES
P
I
T
C
H
E
D
B
A
T
T
L
E
S
Buddy explains!
The straight part
We know that "Hastings and Bosworth perhaps" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hastings and bosworth perhaps = pitched battles.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.