To earn this achievement you will need to complete the Mirage Arena challenge "Light's Lessons." This will unlock at arena level 29, which means you will have to fully complete the arena to unlock this challenge.
Fight spoilers below.
*** Spoiler - click to reveal ***This fight is the easiest secret boss fight in the game, but he can still be challenging. I would recommend once more and second chance to make this easier, and bring a couple of curaga commands. He has a range of attacks that can be dodged and will occasionally become invincible and float in the air while beams of light rain from the sky, which can cause status ailments. He is susceptible to shotlocks if you time them properly, such as when he is charging up his laser attack.
If you want to farm 9999 medals quickly, consider the following:
Monster of the Sea has a very easy farming method which can be used to farm medals (on proud you earn 675 medals per completion, takes about one minute each time). On your command bar, place one Mega Flare and six Mine Squares. When the match starts, use mega flare to clear the room instantly if you're a high enough level, then the Monstro section will begin. Quickly hit two explosive barrels at him (this part may take a few practice tries to get right) and he will become stunned. Swim over to him and spam mine square. Each use of mine square will take away around one full bar of his health. Once all of the mine squares are on cooldown, smack him around to finish the remaining HP off.