TARFU is a close relative of acronyms like SNAFU, FUBAR, and many others. It stands for "things are really fucked up", and like its similarly foul-mouthed cousins, it originated with soldiers in World War II.
In polite company, the F is claimed to stand for "fouled", rather than "fucked". Although why you'd feel the need to use an acronym for "things are really fouled up" is beyond me.
Citations
Ernie Pyle, "
Brave Men", 1944 -
The colonel had a coal-black Labrador retriever named Tarfu. That's one of those mystic military names which you'll have to get somebody else to explain to you".
James Gould Cozzens, "
Guard Of Honour", 1948 -
"On the side of the plane's black nose, spiritedly sketched in dark and red paint, was a cavorting skeleton who carried a nude woman. Winder it, in fancy letters, were the words: Tarfu Tessie".