Illegitimi non carborundum is a mock-Latin aphorism, often translated as "Don't let the bastards grind you down".
Lexicographer Eric Partridge attributes it to British army intelligence very early in the war (using the dative plural illegitimis).
[1] The phrase was adopted by US Army General "Vinegar" Joe Stilwell as his motto during the war, in the form Illegitimati non carborundum.
Illegitimi is presumably the nominative plural of illegitimus meaning "unlawful" or "outlaw" in Latin, but interpreted as English "illegitimate" in the sense of "bastard", in this case, used as a generic insult.
Sometimes (as in The Handmaid's Tale), carborundum is prolonged to carborundorum, as if a Latin second declension neuter genitive plural of a noun ending in -um.