。
She announced her intention to retire.
Literal
She [topic-は] retire intention [is-でいる] [nominalizer-こと] [object-を] announced.
つもり is the standard noun for intentions — ~するつもりだ means 'intend to X.' The variant ~つもりでいる ('be in the mindset of intending to X') is a slightly more emphatic state-of-mind framing: not just having the intention, but actively holding it. Wrapping that whole clause in こと nominalizes it as the object of 発表する ('to announce'). 発表する is a Sino-Japanese verb (発 'release / send' + 表 'display') for any kind of public revelation — research findings, marriage news, business decisions, candidate selections. The Japanese press corps (記者会見) regularly stages 発表 as carefully choreographed events.