word-forming element meaning "bad, ill; hard, difficult; abnormal, imperfect," from Greek dys-, inseparable prefix "destroying the good sense of a word or increasing its bad sense" [Liddell & Scott], hence "bad, hard, unlucky," from PIE root (and prefix) *dus- "bad, ill, evil" (source also of Sanskrit dus-, Old Persian duš- "ill," Old English to-, Old High German zur-, Gothic tuz- "un-"), a derivative of the root *deu- (1) "to lack, be wanting" (source of Greek dein "to lack, want").
Very productive in ancient Greek, where it could attach even to proper names (such as dysparis "unhappy Paris"); its entries take up nine columns in Liddell & Scott. Among the words formed from it were some English might covet: dysouristos "fatally favorable, driven by a too-favorable wind;" dysadelphos "unhappy in one's brothers;" dysagres "unlucky in fishing;" dysantiblepos "hard to look in the face."
The "sh" sound did not exist in Old French, therefore French scribes after the Norman conquest often represented it with -ssh- in medial and final positions, and sch- in initial positions (schape, schamful, schaft for shape, shameful, shaft). But the spelling -sh- has been standard since Caxton, probably as a worn-down form of Middle English -sch-.
In some East Anglian texts from 14c.-15c., x- is used (xal, xulde for shall, should), which would have given the language a very different look had it prevailed, but the London-based sh- ended up as the standard form. The same Germanic sound has become, by natural evolution, modern German and Dutch sch-, Scandinavian sk-.