They appear to be guardians of sorts of the Skyway. They block pathways in the water tubes through which Ecco must pass through to continue on his quest.
This species is very aggressive. They will grab and throw Ecco with their tentacles, chase him, and block his passage with their large body. They are also invulnerable to Ecco's attacks. Unlike normal jellyfish, they do not do any physical damage to Ecco.
They have evolved beyond normal jellyfish in several ways. The first difference is their giant size. They also have the ability to fly and can exist outside bodies of water for extended periods of time. Their bodies appear to have sharp barbs around the head. Their bodies also appear to be considerably more meaty than normal jellyfish.
Usually, there are two paths which Ecco can reach the next part of the skyway. If you are intercepted by the Medusa on one path, quickly swim up the other path and outswim the Medusa before it catches you. The best way to do this is to memorize the paths. You can also use Ecco's sonar to see part of the pathways beyond your presence location.