Serve for life, just like SCOTUS judges. Only way to get rid of a federal judge is to ask for impeachment.
Well, depending on deep his vindictiveness runs, which I assume is Marianas Trench depths, he might try to go for the impeachment.
I think Trump is probably just running into the brick wall of corporate versus government. He thought running the country would be the same as running a company, because as a CEO/president of a company, you basically are an autocrat. You can fire whomever you like without process or explanation, hire/promote with the same freedom, and basically just run things as you see fit, because everyone is your employee, or your subjects, they HAVE to do what you tell them.
He wasn't counting on the idea that some people in government wouldn't consider themselves employees of the President, so much as employees of a government designed to serve the people, and would act that way. He's also never encountered concepts like lifetime appointments for certain positions, so I think he's getting a crash course now in the differences between a country and a company and probably finding that he prefers corporate power over government. A little too late, since he's in charge now, but oh well.