Ghostzilla fights Luigi for the reason that if he defeats him, then Morty will give him the elevator button. Ghostzilla's only means of attack are his fireballs, which Luigi can use the Poltergust G-00 to vacuum and shoot them at Ghostzilla's face (Only the big blue fireballs can damage Ghostzilla, but the red ones can be dodged due to their slow speed.) After his health is depleted, Ghostzilla shrinks into his Goob form, which Luigi can vacuum. After his defeat, Morty, true to his word, gives Luigi the elevator button and Luigi goes on his way, but not before fighting Polterkitty one last time.
At the end of the game, it is revealed that most ghosts in the hotel were were brainwashed by King Boo, and thus were unwilling accomplices. Thus, this might also be true to Ghostzilla. However, his eventual fate is unknown.
While not talkative, Ghostzilla is scary, most likely roaring at Luigi.
Luigi's Mansion: Dark Moon
Luigi's Mansion 3