The Fomorians (Fomhóraigh)
The opposition in every wave, and not simply monsters, since the Tuatha Dé were related to them by marriage.
The Fomorians are the constant antagonist of the invasion sequence, there before the first settlers and fought by nearly every wave. They are usually described as coming from the sea, and the name is often read as something like under-demons or sea-demons, though the derivation is argued.
The popular picture of them as deformed sea monsters is only half the material. Some are described as misshapen, with one eye, one arm or one leg, and Balor's single eye kills whatever it looks on. But Elatha, a Fomorian king, is described as the most beautiful man the Tuatha Dé had seen, arriving on a silver ship with golden hair.
The relationships are the complication. Bres, who ruled the Tuatha Dé so badly, was Elatha's son by a woman of the Tuatha Dé. Lugh, who kills Balor, is Balor's own grandson. Several of the Tuatha Dé marry Fomorians. Whatever these two peoples represent, they are not a clean division between good and evil, and scholars more often read the Fomorians as the forces of chaos, blight and winter against which order has to be established, rather than as a hostile tribe.
They are broken at the second battle of Mag Tuired, where Lugh kills Balor with a sling stone, and after that they stop being a presence in the story.