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Appearing in Yoshi's Story, the Jellyfish are giant jellyfish that live around Yoshi's Island. They are invincible to all known means of defeat, and have a greed for intruders to their waters. Jellyfish come in three colors: Blue, Red, and Green. Blue Jellyfish simply move wherever they want. Red Jellyfish chase Yoshi. Green Jellyfish simply float up and down. Red Jellyfish can sometimes have an item like a Fruit or a Heart Fruit.
Jellyfish only appear in Stage 5-1: Lots o' Jellyfish. Green ones don't appear until the third part.
It is entirely possible that Jellyfish are related to Jelectros, another type of jellyfish enemy found in Super Mario Bros. 3. Pre-Yoshi's Story jellyfish also appeared in Super Mario World 2: Yoshi's Island, going under the name "Preying Mantas".
There are also two Jellyfish Sisters in Mario & Luigi: Superstar Saga. In this game, Jellyfish are depicted as a humanoid, Toad-like, bipedal, and very rare species. As a matter of fact, only two other Jellyfish exist in the game, one as a clerk in the Massage Room, the other at the beach of the Beanbean Kingdom explaining how to cross Oho Ocean.
Later in Donkey Kong Jungle Beat small Jellyfish that looked more like actual ones and not cartoon-like ones appeared as enemies that would shock Donkey Kong.
In Super Mario Galaxy, Jellyfish appear in varouis galaxies, mostly the Deep Dark Galaxy. They float arround the water and hurts when they touch. They can be killed by just hiting they with a shell.