The most common and most likely answer to this crossword clue is the 8 letter word VENDETTA
I've seen this crossword clue in The Times
V
E
N
D
E
T
T
A
More clues leading to the result VENDETTA
- Very English woman engaging daughter in dingdong battle
- Violent quarrel: some revolutionary squatted? Never!
- Old soldier about to finish Territorial Army feud
- Examine volunteers injected with last bad blood
- Unhappy at event including daughter leading to feud
- Aim to break old soldier — army’s vicious campaign
- Feud in Mediterranean capital has purpose for everyone
- Sell Tate off causing feud
- Feud heralds demise for all in Meditteranean capital
- Design probes to check temperature, leading to a prolonged dispute
Buddy explains!

The straight part
We know that "bad blood" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case bad blood = vendetta.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 VENDETTA mean?
VENDETTA noun- A bitter, destructive feud, normally between two families, clans or factions, in which each injury or slaying is revenged: a blood feud.
- (often preceded by personal) A motivational grudge against a person or faction, which may or may not be reciprocated; the state of having it in for someone.