Dusk Diver 2

Story-related and cannot be missed.

Chapter Unlocks (After Chapter 11 boss): Weapon Rank 12 (required for many skills & trophies) & Yumo's Burst EX and special skill D. Rush (see TV Taught Me How to Fight ).
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This trophy is for completing Chapter 11, "Yes, We're Villains". This is a very important Chapter in your Platinum, in several different ways. It's also a very unique Chapter — instead of unlocking Rank 12 in Chapter 12, you will unlock Rank 12 towards the ends of Chapter 11. 

First things first, at the start of the chapter, once you go outside, you'll see that new fissures have spawned all over the human realm. There are 10 in total, and you'll need to close all of them for the Dimensional Fissure Master  trophy.

The majority of the main story quest sees you go through a new location, the East District Passage, along your way to Climax 508. Once you get there, you'll face the main boss of this Chapter — "The Beast of Chaos". After you defeat him and return to the Tumaz Mart, Rank 12 will unlock (thereby allowing you to get Ultimate Craftsman ), as will the last remaining side quests in the game. These include the last companion quests (each of their Level 3 quests), which allow you to earn each of their Burst EXes and special skills as well.

This is the final point of no return. As the game will inform you, "this will be your final opportunity to complete any unfinished business." What this means is... because there is no post-game free roam, this is the very last time you can explore on your own. Once you proceed with the main quest, there is no turning back; you will complete the story and your game will end there. Any trophies you have not unlocked will be voided and you will have to start all over again in a new playthrough to earn them. Because of that, you should stop and take the time to complete all other trophies before continuing with the main story.
 

BOSS FIGHT: "THE BEAST OF CHAOS"
Honestly, the boss fight is incredibly easy, so there's little to say. It has 3 main attacks: it either swipes at you with its paw, shoots a large blue laser at you (that you'll have a lot of time to prepare for and dodge), or it'll drop some swords or pillars from the sky and then, after a few moments, it'll slam its paw down and a bunch of "eyes" will flash on screen and those pillars will turn into lightning bolts. Really though, it's an extremely easy fight, and you can pretty much ignore the boss for the most part and just keep dealing damage.

Just keep attacking the large beast's paw over and over until you break through its armor. Once you do, it will drop its head and expose the ball of light in its mouth. If you have a Burst, pop it and destroy the ball of light. It's extremely weak so it takes a lot of damage, so this should be really quick. If you have a Burst, you can probably kill it in one phase, but if not, just repeat the same thing to get another Break State to finally put it out for good.