Trial Difficulty and Legendary Difficulty comes with Trial cards, a type of fate card that forces you to choose one of three buffs for heroes that enter your dungeon, or a nerf to your monsters.

Trial Cards give the bonus score/exp from every day you have them and they are also affected by the difficulty you are playing, so a trial card that gives +100 bonus score will give +10000 bonus score at Legendary 10 (x100 score multiplier).