This is a pretty straightforward boss fight that occurs at the end of the first level, Jellyfish Fields. The Jellyfish King can only hurt you in two ways; by touching you, and with his ground slam attack. When the fight starts just avoid him until he performs his ground slam attack. Jump over the circular beam of energy he emits when he lands, and then hit him with a basic attack when he's vulnerable.
After your first hit lands, he'll spawn in a few jellyfish. You can take them out or just avoid them, just don't risk losing health if you can help it. Wait until the Jellyfish King ground slams again, and then hit him the same way you did before once he's vulnerable.
He'll spawn in a few more jellyfish, which means if you hadn't taken any out before the battlefield will become a bit clustered. Just keep avoiding the boss until he ground slams one final time, and land your last hit. A cutscene will play, and the achievement will unlock.
EDIT #1: Try to give some feedback if you're going to vote negative. If you don't tell me what can be improved then there's really no sense in voting at all.