(Just a reminder: hi is pronounced like “hee”)
Literally: milk / breast – mother – sun – umbrella
Alternately: Raising a child with the utmost care. By extension, coddling and excess in child-rearing. Raising hothouse children. From the practices, among wealthy Edo-era families, of hiring wet-nurses and shielding their children from the sun with parasols.
Notes: The latter half may also be pronounced hi.karakasa, apparently due to the association of paper umbrellas with Tang China (唐, Kara). Meanwhile, 乳母 on its own has many acceptable pronunciations, including uba, menoto, or chimo, but in this usage it is only read as onba.
This phrase supposedly comes to us from a late-Edo personal essay collection titled 骨董集 (Kottoushuu), translated into English as Curios.