There are two achievements that require additional playthroughs:

Universal Victor: Complete the game on the Universe difficulty level.



Chaotic Conqueror: Complete the game on the Chaos difficulty level.



In order to unlock Universe and Chaos difficulty, the previous difficulty must be completed.



Some of the achievements in this game are almost impossible to do in a single playthrough:

Ultimate Battler: Obtain 100% of all battle trophies.

This guide will tell you how what transfers from one to the next.

The important thing to keep in mind is that it isn't technically a "new game plus" in the sense that we're all accustomed to from RPGs. You aren't starting a new game on top of the old file, you're starting a genuinely new game from scratch, just with the "central data file" compiled during your previous cycle intact (the second file you see writing every time you use a save point).

The databases in the central data file are:

- Battle Trophies
- Weapons
- Monsters
- Ships

In each new playthrough, you'll retain any bonuses you got from any of these databases. You'll be able to create Monster Jewels from the high-end monsters early in the game if you got them to 100% previously.

If you miss something in one cycle that prevents you from hitting a certain requirement, you can go back in another cycle and fulfill the requirements.

Certain information gets written into that file -- but certain information does not. The achievements are just enabled flags : yes or no. Unfortunately, you can't simply find the one chest you missed and not worry about the 200-or-so others.... because it isn't a genuine "new game plus". Rather, I'll have to get every single, solitary chest to get the game to recognize 100% and give me the trophy in question. So if you need to defeat 4000 monsters with Edge, that counter is zero and you need to kill 4000 mobs on a single playthrough.

So in general:

Monster Data %: You can miss some and complete in another playthrough
Spaceship Data %: You can miss some and complete in another playthough
Battle Trophies %: you can miss some and complete the rest in another playthrough.
Specific Battle Trophies are reset each playthrough.

Collecting all chests: Has to be done in one playthrough
Completing all quests: Has to be done in one playthrough
Create all Items: Likely has to be done in one playthrough

The above is modified from GameFAQs[www.gamefaqs.com] with some additional edits. Credit to that guy for the original post^^

Everything below is 100% yours truly.

If you miss a chest or a quest, or one of the unmissable parts from any of the guides available, then you have two options.

1. Load a slightly older save.

2. Ignore those achievements for the rest of this playthrough. Go after that set in the next playthrough. On my first easy run through I had already missed a couple of early quests and chests, so I'm not bothering to focus on those.

3. On your last playthrough? Either complete it and start again on the easiest difficulty, or just start on that playthrough from the beginning again. Especially if you can't do (1).

A small subsection about chests.

Chests have to be opened and remain open. It's not simply enough to open it and for it to close because you have too many of the objects.

Go to your item list, and press <select> on the controller and it will offer to discard one.

As long as you have room for one item in the chest, it will assume it gives you them all, and the chest remains open. A useful hint is that you should never buy 20 of something unless you absolutely need to. Leave 19, so there's no need to fiddle with menus if one comes along.

(So if you are reading this part only a dozen hours into the game and left a few chests, yeah, you need to go through another playthrough.)