It's a welcome and relatively recent development that we can generally talk about breasts as, well, breasts. For long ages they may have been considered desirable, but were not acceptable as topics for polite conversation. Slang and rude terms abounded, but also a rather large array of more or less polite words were used to make conversation more comfortable. Some may remember the classic comic dialogues of Pete and Dud (Peter Cook and Dudley Moore) which spoke of "the busty substances".
In the 19th century it wasn't considered proper at a family meal for a gentleman to ask for "breast" when offered a serving of poultry, and this became "white meat", just as a chicken thigh was "dark meat". Politely one might refer to a person's "front", or "chests". I've even heard an old woman talk of having fallen and bruised her "lungs", and others spoke of discomfort in their Tonsils.
Bust has been around since 1727 and Bosom has generally been considered proper. Indeed, Bosom, sometimes bazoom, is derived from the Sanskrit, and has been used since around the year 1000. Bubbies emerged in the Elizabethan era. In the 18th century there were diddies, duckys, and droopers. Then there were "Cupid's Kettledrums, and Knockers", possibly inspired by the shape of some door-knockers of the period.
Less formally, one might speak of her Cleavage, and photographs which displayed the amiable cleft were known as "Cheesecake". Admiring comments on nipples have been addressed to the Big Brown Eyes, so "She's got a nice pair of eyes" was a rather ambiguous compliment. "Jugs" is a term fondly used in some quarters, and a well-endowed though minor British Princess is reputed to have the family nickname of "Jugs".
Australians have called them Elders, and Norks, possibly derived from the wrapping for a once popular brand of butter, Norco, which showed a cow's udder. Then they have their own rhyming slang, with Tracy Bits, and Brace and Bits, from carpentry. Early South African slang is less well recorded in the literature, though I find references to Mams.
In Cockney rhyming slang, just as feet are "plates" (plates of meat = feet), so breasts were known as "Bristols", after the football team Bristol City. Even earlier, there was "Thousands, from "Thousand Pities" .
Then there's Boobs, Globes, Teacups, Pointers, Marshmallows, and The Twins. Fruity terms have held sway - Lemons, Oranges and Grapefruits, Apples, Pears, and when amply endowed, Melons. Even Coconuts, which added some spice to the old popular song "I've Got a Lovely Bunch of Coconuts".
The there are the motoring terms - Headlights, or Bumpers, or more recently popular again, Hooters. Some aparently mysterious terms arise, like Mosob, which is just Bosom spelled backwards. I haven't found an explanation for Gazungas.