Make a clean breast of it
To make a full disclosure; to confess.
The Oxford English Dictionary defines the noun breast as 'the two soft protuberances situated on the thorax in females'. The meaning used in 'make a clean breast of it' is an earlier and less literal one. The 'breast' there is the seat of the one's emotions and secrets; one's 'heart'. To disclose this openly was to clean one's heart of impurity. Any mention of breasts now is likely to be a reference to the 'soft protuberances' - we are more liable these days to 'get something off our chest'.
'Make a clean breast of it' is known since the 18th century and is cited by Cameron in The Scots Magazine, 1752:
"He pressed him... to make a clean breast, and tell him all."
The phrase parallels the later, 19th century American 'come clean'.