Use violence or extreme measures.
The expression 'get medieval' was coined in the USA is fairly recent years. It joins a list of figurative phrases of the 'become crazy' form. These include venerable expressions like 'go berserk', 'run amok', 'go haywire' and, more recently, 'go postal'.
The allusion in 'get medieval' is clearly to the forms of torture that were in use in the Middle Ages, the best-known of which was the rack. This grisly stretching apparatus was used to extract retractions of faith from both Protestants and Catholics during the 15th and 16th centuries in England. A notable victim was Cutbert Simson, who is shown in the accompanying image, which records his torture in 1558. He was probably relieved when he was released from the rack, but not for long - he was burned at the stake soon afterwards.
The person who brought the phrase 'get medieval' to the public's attention is Quentin Tarantino, who, with Roger Avary, wrote the screenplay to the 1994 film Pulp Fiction. In the film, the character Marsellus Wallace swears revenge on an attacker:
I ain't through with you by a damn sight. I'm gonna git Medieval on your ass.
Tarantino leaves it to our imagination what the revenge will be but, as Wallace says it is going to involve "a pair of pliers and a blow-torch", we can assume a degree of unpleasantness.
Tarantino and Avary didn't coin the phrase however. It was in occasional use by the 1970s. The earliest use that I can find of it is in another form of pulp fiction, a cartoon strip in the Ohio newspaper The Lima News, October 1971. The cartoon suggests that the expression wasn't then used as a reference to extreme violence.
See other phrases that were coined in the USA.