Nightmare

The Nightmares are the main antagonists of, monsters that invaded the Wind Fish's dream world of Koholint. They seek to rule the island by preventing the Wind Fish from ever being awoken with the Eight Instruments of the Sirens. To that end, eight of the Nightmares have taken each of the Instruments and hidden them within their lairs, accessible only by the Nightmare's Keys hidden within their monster- and trap-filled labyrinths. Most of these Nightmares are intelligent enough to speak to Link, the "outsider",, and attempt to scare or warn him off of retrieving the Instruments, going so far as to reveal the true consequences of his actions: the destruction of the island and everything on it. Despite their warnings, Link retrieves each of the Instruments and even survives the final onslaught of the Shadow Nightmares at the Wind Fish's Egg, allowing him to reach the Wind Fish's resting place, play the Instruments, and awaken the sleeping deity.

Theory
While only the eight main boss monsters and the Shadow Nightmares are referred to as Nightmares, other monsters on the island become more active once Link arrives, and are found throughout the dungeons and world of Koholint. The Grim Creeper, despite not being the main boss of the Eagle's Tower, rides the Evil Eagle and speaks to Link, and therefore is thought to also be a Nightmare.