He can't fire a federal judge. There is a due process for impeaching a federal judge from the bench. Neither can Department of Justice (which is part of the executive branch), it is one of the best preserved traditions of our Checks and Balances, despite some of rulings are not agreed by majority (do I have to bring up the stupid ruling of Judge Persky on the People vs Turner case). Therefore, we can't fire or replace a Supreme Court judge except the Congress.

You are probably mistaken that for the firing of the acting AOG Sally Yates for mandating Department of Justice to not to defend Trump's travel ban executive order during her tenure, and the termination of New York-based U.S. Attorney Preet Bharara who was known for going after Wall Street scandals (and who, according to Trump, did not return Trump's calls multiple calls).

--Edit--

I found [1] to be an interesting article on whether impeachment of a judge is limited to Congress.

[1]: http://www.yalelawjournal.org/forum/removing-federal-judges-...