The phrase "shady business" refers to activities or dealings that are dishonest, unethical, or possibly illegal. It suggests that something is suspicious or not trustworthy.
Beware of shady business practices used by this business. (yellowpages.com)
While in town, they learn of shady business considering their late mother's ranch, as well as the murder of their father a few years prior. (rottentomatoes.com)
He may like to do shady businesses but will never name a player so blatantly in public. (therepublikofmancunia.com)