The Scathach bonus round rule is one of the many rules that can be applied during the Bonus Round episodes. It has a rare chance to spawn on floor 3 and further for every character (more common on floor 4 or 5), although it is rarer than other rules like it. The rule cannot appear at the same time as the Skeleton Bonus Round rule.
When the rule activates, the player will be inflicted with 1 Curse at the start of each turn, meaning that the initial equipment used will have a chance to fail. It'll end up pretty bad if the Banshee or Warlock rules are set in place as well, since you'll face the constant terror of a piece of equipment backfiring on you.