If you are new here, then you're probably wondering what all these missions are about and what does one actually needs to do to complete them. Now I'm sure that there are some threads on the forum here that explains all that, but I'll add in the explanation here as well, just in case.
Well, here we go:
● LUX Missions:
These missions are always present on Chi and are updated every Monday JST. After some consideration it was decided that I will leave the usual LUX missions list at the end of this post, along with the Union missions that come next

I will post a special event LUX mission list, if there is any, <em>before</em> the usual one. So, if you see any other LUX Missions spoiler in this post, then it would mean that the standard weekly missions are temporarily suspended until the event passes
There are times when these missions are replaced by a new set due to some Event of sorts. Those missions I will cover in my thread
So, what you need to know about LUX? First of all LUX is the energy thingies you get from defeating Heartless and more importantly from Attacking the Raid Boss. Basically - the more damage you do, the more LUX you get. That and the bonus LUX acquisition rate from your Assist cards and the LUX Up time (LUT) that doubles the LUX you get. The timeframes for the LUT are as follows:
[1] 01:00 - 02:00
[2] 07:00 - 08:00
[3] 12:00 - 13:00
[4] 19:00 - 20:00
[5] 22:00 - 24:00
Please remember that these times are all JST!
● Union Missions
Every week the total wins of the Unions are calculated and ranked – the better place an Union gets, the better the Missions and their Rewards. They <em>usually</em> don't change, unless it is some special occasion.
● Guilt Target Missions:
These missions require you to defeat a number of certain heartless to get Guilt Points from them (1 - 5 at a time). And by getting Maximum Guilt for those heartless (you can view your current progress by pressing Guilt Target (ギルトターゲット) button in the main menu) you'll fulfill the requirements of these missions, getting the respective rewards.
But that is not all! Guilt Points give Bonus attack power to your character while fighting a Raid Boss! Specific heartless, depending on how difficult it is to defeat it, gives you a certain amount of that Bonus per Guilt (BpG column in the table) which is then multiplied by your total Guilt Points for that Heartless.
A particular thing of notice is that when you max out the Guilt for a Heartless, the total bonus you get from the guilt is multiplied by 1.5! Yay more attack power!! And speaking of that - the total Guilt Bonus that you have gets multiplied depending how much BP you use to attack the Raid Boss: x1 for 1 BP, x2.5 for 2 BP, x4 for 3 BP and a whole x5 for the first attack, which is free of BP-charge
But these missions are important not only for getting the goodies from the rewards (which usually are Mog Medals that you can use in Mog Shop (モグトレード) to buy stuff and Orichalcum (オリハルコン) to strengthen your weapons) , but for getting LUX rewards as well. So hooray Guilt!
Another important thing you should know is the Guilt Up time (GUT) - during which you will always get 5 Guilt Points when you defeat a Heartless. Those timeframes are:
[1] 11:00 - 11:30
[2] 18:00 - 18:30
[3] 21:00 - 21:30
Please remember that these times are all JST!
● Guilt Help Missions:
As of maintenance on 6/15/2014 S-E decided to add these new types of missions, which basically mean that:
You need to go to your Team menu (チーム), press the Member List (メンバー一覧) button under your team's score, then press the Guilt Help (キルトヘルプ) opposite to the team member's name, then Help (ヘルプする) button in the next window. You will be transported to "another player's world", where you will be able to battle heartless, receiving EXP, LUX and Munnie for their defeat. No Guilt (which goes to the other player) or Card Drops will be awarded to you. What these missions require you to do is defeat a number of specific Heartless in a player's world. The heartless that you defeat should count towards the mission requirements even if that player has maxed out the guilt of that particular Heartless. When you are done, leaving is as easy as pressing the Finish Helping (ヘルプ終了) blue button on the upper left side of the screen. You'll be back to "your own world" and hopefully live happily ever after. Happy hunting~
● Raid Boss Missions:
There are a few types of these kind of missions - Daily ones that renew every day, Weekly ones that renew every week and also Chirithy's Orders ones, that are also renewed every week or so. These missions may require you to do something as easy as attacking a Raid Boss a certain number of times, Defeating a certain number and\or level of Raid Boss or Raid Boss Subspecies, which are colored red when they appear and have a 100% next to them on the Team screen (actually participating in a successful Raid Boss .. raid that leads to the RB's demise. And that means that you need to land at least a single hit on it). The Subspecies (or Subs) are spawned when your team defeats a number of normal RBs in a row so that the per cent counter on the left reaches
● Heartless Missions:
From time to time S-E holds events that add new Heartless to the map. And these missions are oriented on defeating a certain number of those new Heartless. As easy as that

The list and pictures (yay pictures!!) of all of them baddies can be found
here
● Trial Missions:
These missions put constraints on player while battling Heartless. These constraints so far have been limiting the number of Continues the player can use while fighting the Heartless and even harder ones that limit you to defeating a certain Heartless in a certain number of turns. There's also a constraint of fulfilling those conditions a certain amount of times in a row. Yeouch, talk about player cruelty
