I Can't C challenge requires you to play through a round with you being the only one visible ranker in the ladder table.
In order to make yourself the only one visible in the ladder table you would need to disable the "Show All Ranker" option in the Options menu and set all the other "Show..." options to 0:

This way the ladder table will turn from something like this:

Into this:

Since this run will pretty much be a normal playthrough, winning is very possible. In fact, you might even be able to win some ladders and finish quite high overall in the competition for Ladder Champion trophy.