The Storm Jellyfish will not spawn on its own. The only way to summon it is to use a Storm Jelly. It can be used anywhere at anytime.
Flies through the air and chases the player at roughly top base sprinting speed, but has to take wide turns if the player gets around it. It is unimpeded by solid blocks.
Periodically shoots slow moving bolts of electricity that do roughly twice as much damage as contact with the Storm Jellyfish. Also inflicts the Electrified debuff.
Summons a Flying Jellyfish every so often that has the exact same movement pattern, and has contact damage as strong as the Storm Jellyfish's bolts.
Creates Orbs that arc lightning at you that do about as much as the bolts
The biggest threat in the fight is the electric bolts. Their base damage is a decent threat alone, but Electrified will quickly drain your health, and does so four times as fast if you're moving left or right.
A pair of Lightning Boots will allow you to easily outpace the Storm Jellyfish. If your arena isn't super long, use the rocket boot function to jump over the Storm Jellyfish; you should be able to just dodge it, and it'll take a large turn to get back on track.