Aside from the 20 to 30 monsters you can miss in Nene's Fortress (end of disc 2), there are three elusive monsters you will have to search for once your party gets a mechat on disc 3.
These monsters are super tough and can do more than 999 damage to everyone in your party. Increase your shadow class ranks or expect to die very quickly.
Gold Mecha Robo: The Ancient Factory 1F. Past the first conveyor belt.
King Poo Snake: In the Ancient Ruins Cave. Defeat the Jumbo Poo then the Corrosive Poo for this enemy to appear.
Gold Poo Snake: Defeat the King Poo Snake and the Platnum Poo. The Platinum Poo is on one of the three south and southwestern island archipalageo and the Gold Poo Snake will rarely appear (on that same set of islands), giving you that chance to destroy it.