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First stretch goal is done, meaning that the first chapter and UI are being retranslated, and we might manage the second as well.  Stretch goals 3 through 5 are probably beyond what the Kickstarter will reach.

Alright, so, the moon phases will alternate in this order: Fire>Ice>Wind>Earth>Lightning>Water>Light>Dark. Fire element units are stronger during a Fire moon and weaker during an Ice moon. Ice element units are stronger during an Ice moon and they're weaker during a Fire moon. This kind of dual relationships works in pairs for the aforementioned elements (Fire and Ice, Wind and Earth, Lightning and Water, Light and Dark). Eight elements, sixteen turns for a complete cycle.
Since we have Day and Night phases, the moon takes one full day (or 2 turns in-game) to change. So you'll have:
Turn 1: Fire (Day) - Assuming that you picked Fire moon as your starting moon phase when you started a new game

Turn 2: Fire (Night)

Turn 3: Ice (Day)
Turn 4: Ice (Night)
(...)
Turn 16: Dark (Night)

And then the cycle restarts at Fire (Day). If you're wondering what those numbers mean, 1 is the current moon phase, 2 is the next moon phase, and 6 is the previous moon phase.

Here next to Attack, you can see that it's currently Earth moon.
Hope this helps clear things up.
 

Thank you for reading it!
Not sure if you can read Japanese, but you can find the unofficial wiki here. If you wish to check what your ranking would be, you can check it over here. Making quick use of google translate:

Element of the day (or moon phases) is easy to check out, it's right above your resources. I understand that there's a lot of information so it's not difficult to miss out on these things. It's also possible to check what the element of the day it is during battle, though.
If my review urged them to finally reveal the stretch goals, that would mean mission accomplished, I suppose. I really hope we hit that first mark, but...
I'm not sure if "Parts featured..." refers to a retranslation of the prologue and Chapter 1, but perhaps it can be mended by an editor. I still do hope that skill descriptions get fixed since it's kinda ridiculous when half of the script is cut out in a translation. Either way, I'm really happy about the announcement, but I wish that the reTL had its own stretch goal, since the other items bump the price up a bit.

I suspect they don't have stretch goals, with the Money Pool taking their place.
Anyway, nice review, hope they read it, but one thing I want to ask is where the "unofficial wiki" is, as I'm trying to find it so I can rank my own performance.  Also, in addition to your criticisms, a clearer explanation on how to tell what element the day is would be great.  I've yet to figure it out.
Edit: Never mind, they've revealed the stretch goals.  Wonder if your review had anything to do with it?  Since part of Stretch Goal 1 is redoing the parts released in the demo by Arunaru...