I imagined Parallax being defeated like in "Green Lantern: Rebirth". Hal Jordan, Sinestro, Kilowog and Tomar-Re are fighting Parallax in Earth or Oa or Space, and basically, Parallax starts to project their fears in front of them. Hal and his father's death. Tomar-Re and his failure in saving a planet (Nod to Krypton). Kilowog and possible death of his trainees. Sinestro and Korugar is turmoil and chaos. Then, they all start to chant the Green Lantern oath, and exorcise their demons.
Hal says he doesn't care if his father died with fear, because he died a hero and that's what matters.
Tomar-Re comes into grips with his mistakes and says that, although it doesn't make it up, he saved countless lives beyond those he failed to rescue, and that counts for something.
Kilowog claims that he is a damn good trainer, and his students are most likely to kick their enemies' asses than to be defeated for them.
Sinestro, however, garantees that he will never allow Korugar to crumble into chaos. No matter what happens, order will overcome chaos, and Parallax will pay if he gets in Sinestro's way.
They all exorcise Parallax from their bodies and transport his essence, through their rings, to the Central Power Battery in Oa, where the Guardians trap the essence of fear itself into the Battery, completelly overpowered by the ability of all Lanterns to overcome fear, too weak to talk, move or act.