The demon that Angelus tries to awaken in season 2 is Acathla. In Buffy the Vampire Slayer, Acathla is an ancient stone demon whose awakening can open a dimensional vortex and pull the Earth into a hell dimension.
Angelus learns that Acathla can be activated by a vampire with a human soul, but once the demon awakens, only the sword of a vampire with a soul can close the portal. After restoring his soul through Drusilla’s ritual, Angel is briefly able to stop the threat, but Willow’s spell is undone and Angelus returns. He then carries out the ritual and awakens Acathla.
Buffy ultimately kills Angelus with the sword just after Angel’s soul is restored, sending Angel through the portal and closing it. The other options are important Buffy villains, but they are not the demon connected to this season 2 apocalypse plot: the Judge is a separate demon, while the Master and the First have different roles in the series.