I agree with harey. As was said earlier, you can rule out the Drummer from being the Truth teller because he said he tells truth and lies, and you can rule out the Piper as being the Truth teller because he says someone else always tells the truth and there's only one Truth teller. So there are three possible Truth tellers.
(1) If the Jester is the Truth teller then the Piper must be the Liar, as Babysnoot said, but that's not enough to rule out other possible truth tellers.
(2) If the Juggler is the Truth teller then you know the Drummer must be the Liar. Since the Drummer can't be the Truth teller, and the Truth teller said his statement that he tells both truths and lies is false, the only thing the Drummer could be is the Liar. This kind of works against Babysnoot's argument.
(3) If the Bear is the Truth teller, then we know the Juggler isn't the Liar but I can't narrow it down more than that.
I also considered the possibility that the statement that the other three "tell a mixture of truth and lies" means that there must be both some true statements and some false statements among the three, but that still doesn't help. If the Drummer and Juggler are mixes then the Drummer's statement is True and the Juggler's statement is False, so any solution excluding them as Truth teller and Liar would work. And for the Drummer = Liar / Juggler = Truth teller scenario, you would have the Jester's first statement be True and the Piper's statement be False, so that doesn't rule anything out.