Ultimate Stages (formerly Soulmaster battles) are special battles designed mainly for high level players. These battles are available, most often, as part of an event and are open for only a day. The bosses of these levels will always drop their card.
Nightmare Battles are a difficulty introduced with the Power Release of some Sealed Lords, and the Ultimate Greek Lords. These battles are designed for even higher level players. The bosses of these levels will always drop their card. The battle with the related PR material is also a guaranteed drop.