In The Strange Case of Dr. Jekyll and Mr. Hyde, what did Mr. Hyde do after he was transformed?

The broadest and most comprehensive answer is, whatever he wanted.
A slightly more specific answer is, Mr. Hyde did whatever Dr. Jekyll wanted to do but didn't do, because he was concerned about his reputation and social standing.
To get more specific, and get down to details, Mr. Hyde did a number of things readers are explicitly told about.
Mr. Enfield tells the reader the first of these shocking things in the first chapter: when walking late at night, Hyde trampled a little girl to the ground. He stomped on her so hard people could hear her bones shatter.
Another specific and shocking action Hyde took was to beat Sir Danvers Carew to death. He was talking to this respected older gentleman on the street, and then he suddenly beat him to death with Jekyll's cane. (This is described in the chapter titled "The Carew Murder Case.")
Besides doing these things, Hyde did them in public, with witnesses. That's the opposite of Jekyll, who tried to hide his sins and vices.
Those are the main specific actions. Jekyll also tells of Hyde's actions in general in the final chapter. Hyde lusted to cause pain. He feels younger and more sensual. He's rude, and so on.