How does CR work for what should be big ‘solo’ monsters? How would a DM calculate CR for a big villain that he or she has created? The CR of a monster is based on the level at which a party of four player characters could fight that monster and have a moderate-to-challenging fight. So, for the big, solo monsters that you fight, four-on-one serves as the baseline for the CR system, and CR represents about the level at which the monster starts to pop up in adventures (there’s some leeway in this, of course; you could fight something of a higher CR, but it becomes significantly more challenging). If you’re fighting monsters in larger numbers, they’re almost certainly of a CR that is lower than player character level.
As for calculating the CR of a villain, you’ll do that just like you would with any other monster: by comparing the villain/monster that you’ve designed to a set of baseline values to determine its CR, similar to how monster design worked in 4th Edition. We’re going to present a set of guidelines that you can use to gauge the CR of a monster, whether built like a player character or built just as a normal monster. (More on this in the next answer.)