Dual Hearts (デュアルハーツ) begins with a treasure hunter named Rumble learning about a treasure, the Dream Stone on Sonno Island and setting out for it. At the same time, Tumble, who is a magical dream creature called a baku, is summoned by the Dream Queen to protect dream orbs. They both come to the same island and after a strange twist of fate become partners. Bakus can exist both within the dream world and the real world, and Rumble uses Tumble to travel into different peoples' dreams searching for the dream orbs. Most of the dreams become nightmares full of dangerous monsters whom they must fight before proceeding to bosses.
Bosses in order of appearance:
Moneybags: A bag of cash in Val's dream.
Magdali: An art teacher in Florence's dream.
Lizardman: A water-based lizard monster in Yuri's dream
Snow giant: A snowman wearing a winter coat in the old man's dream.
Cascey: A winged seashell that controls the seasons in Lillian's dream.
Statue knight: A cyclops knight statue in Toma's dream.
Dark Mist/Possessed Teddy Bear: A teddy bear that has been possessed by the dark mist in Chiffon's dream.
Lord Demios: The "Bad guy" in hannah's story book in Hannah's dream.
Source: Wikipedia, "Dual Hearts", available under the CC-BY-SA License.