Dream Mirrors were shown only in the fourth season of the anime, and were not in the manga at all. They existed within the heart of a person who had a beautiful dream of some kind, and the Mirror was connected to their dream; it appeared to be either a physical manifestation of the dream or at least a means with which to view it.
When Pegasus fled with the Golden Crystal, he hid within someone's Dream Mirror, and the Amazon Trio and Amazoness Quartet were given the task of finding the one in which he was hiding. They would find someone with a beautiful dream and force their Mirror to manifest, then look into it to see if Pegasus was hiding therein.
It appeared that Dream Mirrors were similar to Pure Heart Crystals in that the owner of the Mirror could not live once it was removed. In episode 149, when the Lemures Mister Magic Pierrot accidentally shattered Usagi's Dream Mirror, she fell unconscious, and would not have revived if Fisheye and Tiger's Eye had not sacrificed their power to restore it.
Dream Mirrors normally appeared as mirrors with pink frames with a purple bow at the top, except for Pegasus's host mirror, which was gold in color due to the influence of the Golden Crystal.
An exception to this was found in episode 156. The artist Kamoi's dream was to paint pictures as he saw them, as he felt that making people look prettier than they really were was painting a lie. When he painted CereCere as prettier than she really was, he started to feel unwell, and when his Dream Mirror was revealed it was grey and tarnished. She and her Lemures, TogeToge Jou, remarked on its unusual appearance, and the Lemures refused to eat it because of that.
Removing Dream Mirrors
The Amazon Trio counted "1, 2, 3" in order to remove someone's Dream Mirror, with each number corresponding to a different step in the process. When they counted 1, a large, coffin-shaped red slab would appear behind their victim. When they counted 2, cuffs would appear over the victim's hands and feet, restraining them to the red slab. When they counted 3, the victim's Dream Mirror would reveal itself. They would then physically look inside the Dream Mirror to search for Pegasus; this process seemed to not only cause the victim pain, but to allow the Amazon Trio to actually see what their victim's dreams were, as they would occasionally comment on the victim's dreams while searching for Pegasus within the Mirror.
The Amazoness Quartet would use a pool cue to shoot their Amazon Stones into their victim's torso in order to knock out the Dream Mirror inside. Instead of looking in the Mirror, they would only look to see if the Mirror was golden in color, which would represent the Golden Mirror with Pegasus within it. If unsuccessful, they would then try to get their Lemures to eat the then-unnecessary Dream Mirror.