The Nightmare Mother is the boss in the first section of Gate's laboratory in Mega Man X6. This mechanical entity is the source of the Nightmare Phenomenon, discovered by Gate as a mere fragment of Zero's DNA but extensively modified to become this monstrous form.
The eyes of the Nightmare Mother move around the boss-room in a circular pattern, each one always on opposite sides. (Speed of transition between walls depends on difficulty.) Every once in a while, they will stop to launch their attacks. The attacks include firing blue energy balls from overhead that fly across the screen and strike the floor with thunderbolts, and smaller energy balls that bounce off walls. They can also fire shots similar to the Goo Shaver from Mega Man X5 that travels down walls and across floors. Occasionally, they will stop stacked on the same wall. While the one on top fires small energy balls from above, the other will fire a ball of flame at the floor, causing it to erupt in flames. When one of the two eyes are destroyed, the empty shell of DNA will slam into the walls while the other one launches attacks, further limiting the "room" the player has to maneuver.
The Nightmare Mother's only vulnerable area are the mechanical eyes, which are weak to the Metal Anchor or Rakukoujin. X with the Shadow Armor can deal massive damage to the "eyes" just by unleashing his Charged Shot or the Giga Attack on it while it is exposed.
The way that they can only be damaged while attacking is very similar to the Devil series of robots (e.g., the Yellow Devil) from the original Mega Man series.