The most common and most likely answer to this crossword clue is the 6 letter word MAMMAE
I've seen this crossword clue in The Guardian
M
A
M
M
A
E
Buddy explains!
The straight part
We know that "Breasts" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case breasts = mammae.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 MAMMAE mean?
MAMMAE noun- The milk-secreting organ of female humans and other mammals which includes the mammary gland and the nipple or teat; a breast; an udder. (plural: mammae)
- An accessory cloud like a mammary in appearance, which can form on the underside of most cloud genera