The Condorcet criteria itself is easy. If a candidate would beat every other candidate in a one-on-one matchup, that candidate should be the winner. There, that's it.
That's really how it should be described. And then as a next step, we can then describe "tiebreakers". Instead, wikipedia (and others) describe Condorcet only in terms of their tiebreakers, making Condorcet methods themselves appear flawed[1].
You see, loops are possible. In a vote, it's possible that A would always beat B, B would always beat C, and C would always beat A. And the various Condorcet tiebreakers (like Schulz) are ways to resolve those situations.
But the point is, if that happens, the vote really is accurately uncovering an indecisiveness that actually exists in the voting population. So it makes sense that a "tiebreaker" would be non-ideal in some sense. And they all are in some way. The problem is not with the tiebreaking methods. The problem is with the voting population.
I've always thought a good voting system would be the following:
First, rank the votes. If a Condorcet winner exists, the election is over. If not, restrict the candidate pool to the Schwartz set, and start a new round of campaigning so the voting population can research more and better educate themselves.
[1]. Yes, we can argue that the Condorcet criteria is "perfect" if a Condorcet Winner exists, with one caveat: it implies the value that all votes have equal value. If you have that value, it's a logical implication that the Condorcet Winner (if it exists) should be the winner. But other values are possible, such as a utilitarian mindset of wanting to meet greatest social utility, such as some voters being far more passionate or educated than others. Following those implications bring up other tricky problems, though.