Mud Monster - a large monster made of brown mud all around his body. He usually only shows a single tooth in his mouth, and he does not have eyeballs, but has eyeholes. In the game, his name is Frank. He could be a reference to Clayface, a Batman villain.
Green Sea Monster - a mutated green creature with a face in his large yellow eye. He has another eye on his arm and has a snake mouth and nostrils on his chest. In the game, his name is Shapeshifter.
Purple Hag - a purple fish-like being with messy hair and purple skin. He wears red clothes and has a long beard. His name is Phorkys.
Neptune and Amphitrite are invited to the party with their monsters. SpongeBob asks Amphitrite if anyone is missing in the party. The Purple Hag, the Green Sea Monster, and the Mud Monster are thinking who is missing and are confused.
Triton appears shortly after and traps with Mr. Krabs, Squidward, Amphitrite, and Neptune inside of a cage. SpongeBob and Patrick work together to free them, with Neptune being very angry at Triton. After Neptune sees the destruction created by Triton outside, he then proceeds to hug his son for doing "the right thing." SpongeBob, Patrick, Amphitrite, Squidward, Mr. Krabs, and the Monsters from the Party are all cheering for the two.
The Mud Monster, the Green Sea Monster, and the Purple Hag decide not to go to Atlantis and stay on the ground.
In The Clash of Triton PC Game, the monsters are given names and Triton uses them to cause destruction before SpongeBob and Patrick defeat them.
They also appear in the short "SpongeGod" where they are eating with Neptune and Amphitrite while Patrick talks to SpongeBob about becoming a god.