To make short work of - to give little consideration to.
Shrift? Not a word you hear every day. In fact, apart from in this expression, it is now so rarely used that it's hard to think of a shrift that isn't short. The verb form, shrive, is also now an almost forgotten antique. A shrift is a penance (a prescribed penalty) imposed by a priest in a confession in order to provide absolution, often when the confessor was near to death. In the 17th century, criminals were sent to the scaffold immediately after sentencing and only had time for a 'short shrift' before being hanged.
Shakespeare was the first to write it down, in Richard III, 1594.
Dispatch, my lord; the duke would be at dinner:
Make a short shrift; he longs to see your head.
It doesn't appear again in print until 1814, Scott's Lord of the Isles:
"Short were his shrift in that debate. If Lorn encounter'd Bruce!"
That seems an uncommonly long time to wait for a phrase that is in regular use. We can assume that, given the gap, the phrase wasn't part of the language in Shakespeare's day, or for some time afterwards, and that he coined it himself. Some sources cite it as '14th century', but neglect to offer any evidence to support that.
It didn't migrate across the Atlantic quickly either. The first citation there is from the Adams Sentinel, Gettysburg, Pennsylvania, August 1841:
"The negroes were to be tried on Wednesday, and it was believed that a short shrift and a speedy doom would be awarded to the guilty."
See other phrases and sayings from Shakespeare.