Goddess of the Full Moon, Tsukuyomi is a standout amongst <<Oracle Think Tank>> Grade 3s for several reasons, the first of which is her innate 11000 power, something no other card in the clan can boast. Additionally, she has two to three opportunities per game to draw two cards and filter out the least useful (or sometimes, the most necessary) card in your hand, sending it to the soul. Naturally, when you combine these two aspects of the card with each turn's normal draw and Twin Drive, striking the Full Moon when it matters most can be nigh-on impossible, and her army is just going to keep advancing no matter how many allies fall in battle.
Much like Spectral Duke Dragon, this Grade 3 is the end of a ride chain, so in order to get the whole picture of what it really does for the player, one must examine where everything begins, and what happens as the player crawls their way up to the top.
Godhawk, Ichibyoshi begins the game by searching for Goddess of the Crescent Moon, Tsukuyomi amongst the top five cards of the deck. If found, the Crescent Moon can be rode on the spot without any commitment from the hand. If not, nothing was lost - the normal ride is still possible. The cards that are viewed are sent to the bottom of the deck in any order the player chooses. At this stage, the player knows a few cards they won't expect to see for awhile, and they've perhaps scored a free ride for doing nothing. It's quite powerful for a first Vanguard, as it nearly doubles one's odds of success in riding the matching Grade 1 when compared to the first Vanguards of other ride chains. Granted, there's no immediate reward for that success, but everything adds up later. The odds of starting with at least one Crescent Moon, without a mulligan, are slightly over 65%. With it? Expect a good three out of four games to start well.
Once Goddess of the Crescent Moon, Tsukuyomi lands in the Vanguard Circle, the player then has the opportunity to hunt down Goddess of the Half Moon, Tsukuyomi in the same fashion on the following turn, and again, sends any cards that weren't Half Moon to the bottom of the deck in any order. That's another five cards which can be ruled out from more immediate play possibilities, and another possible ride for nothing. Crescent Moon holds a respectable 7000 power, which allows her to attack most other Grade 1 units by herself. Further copies serve as solid boosters for attacks made later in the game. The second generation ride chains lack this luxury, as their Grade 1 units hold a mere 6000 power in the rear-guard.
Goddess of the Half Moon, Tsukuyomi's descent begins the real payoff for one's dedication to the chain. When ridden, Half Moon lets the player Soul Charge twice so long as Ichibyoshi and the Crescent Moon are already present in the soul. Of course, they typically will be. This Soul Charge is an important step in fulfilling the requirement to activate Goddess of the Full Moon, Tsukuyomi's skill; it places her pilot at a cumulative soul of five, leaving just one more to come in from external means. Do note that six <<Oracle Think Tank>> soul needs to be achieved, so there's no better reason to keep the deck free of tech from other clans. Half Moon has the standard power of 9000 for a Grade 2 unit, so it's not a terrible rear-guard if need be. As with Ichibyoshi and Crescent Moon, Half Moon looks to grab Full Moon each time she's in the Vanguard Circle at the start of the ride phase, sending one more batch of four or five cards to the bottom of the deck in the process. One might not ever see those cards again and as such needs to plan accordingly.
There's a certain bizarre phenomenon almost exclusive to the Tsukuyomi deck in which missing Grade 3 does not put the player at an immediate disadvantage. In fact, there are times when this is beneficial because another set of four of five cards are sent to the bottom of the deck for each turn Grade 3 is not achieved. There will come a point in longer games where Tsukuyomi's pilot knows the exact contents and the exact order of their deck, because they've already seen those cards thanks to the abilities of Ichibyoshi, Crescent Moon, and Half Moon. This allows for the option (key word) of a deadly finish with a barrage of double triggers each turn, provided the cards were placed in a fitting order to do so from the start and that the Tsukuyomi player can reach them. Of course, there are plenty of things that make this feasible!
Goddess of the Half Moon's soul charge two skill
Goddess of the Full Moon's draw two skill
Psychic Bird's draw one skill (which enables the Full Moon)
Oracle Guardian, Red Eye's soul charge one skill (which enables the Full Moon)
Oracle Guardian, Blue-Eye's draw one and send one to the bottom skill
Petal Fairy's drop one and draw one skill
Battle Sister, Cocoa's check the top card and send it to the top or bottom skill
CEO Amaterasu's soul charge one and send the top card to the top or bottom skill
CEO Amaterasu's draw up to five skill (albeit, this is super situational)
Dark Cat's both players draw one skill
In fact, the very notion of Tsukuyomi being able to do this will, at times, cause attacks to be thrown at rear-guards and make things awkward, so tread carefully!
It's quite possible to win the game through sheer advantage and power, though. Weather Girl, Milk; Silent Tom; and Battle Maiden, Tagitsuhime make for some crazy pressure.
Of course, I wouldn't be too credible if I only spoke in ideals, so it's time to go over the deck's most common pitfalls and how to address them should they arise.
Failing to ride Goddess of the Crescent Moon, Tsukuyomi on the first turn
It happens, it sucks. There are two options; ride a different Grade 1 unit, or wait a turn in hopes of the Crescent Moon coming out to play. The latter is most feasible when playing first against a conservative opponent, while the first is the usual approach. Remember here and now that the five cards sent to the bottom of the deck aren't going to come back, and that three soul are going to be required to turn Full Moon's drawing skill online. Any copies of CEO Amaterasu, Oracle Guardian, Red Eye, and Psychic Bird are precious commodities that need to stick around to fulfill this task.
Failing to ride Goddess of the Half Moon, Tsukuyomi on the second turn
This hurts, perhaps to the same degree as missing the Crescent Moon. From here, it's the same story; ride a different Grade 2 unit (Oracle Guardian, Red Eye if given the option) or wait for her to appear, and again that latter option is best used when taking the first turn of the game. If there is no Grade 3 on hand, the latter option essentially becomes the only one, as even if a different ride were to be used, there would be no means of securing a Grade 3 Vanguard.
Failing to ride Goddess of the Full Moon, Tsukuyomi on the third turn
As explained earlier, this is not always fatal. The player has another shot at it next turn and can stay in the game by playing a solid defensive game. If possible, riding CEO Amaterasu instead tends to help in accelerating the deck further and keeping a good offense. She is quite prone to attacks by comparison to Full Moon, however. An extended stay could spell doom if the top of the deck isn't trigger-heavy. Ride Full Moon at first opportunity, and try to threaten the megablast if possible.
All/too many copies of a required Tsukuyomi were sent to the bottom of the deck, and/or damage checked, and/or soul charged
Odd, but not out of the question. In this event, Lozenge Magus can shuffle the deck after boosting, sending the remaining copies to random places in the deck rather than the bottom, so they have a chance of showing up as necessary.
Riding Goddess of the Full Moon, Tsukuyomi without Ichibyoshi, Crescent Moon, and Half Moon all present in the soul
That terrible, terrible 9K. Most front line attackers can hit this without a boost, and it is top priority to make sure Full Moon's debuff does not make an impact on the game for an extended period of time. Keep in mind that, once her skill to draw is online, it's possible to place any missing pieces of the chain into the soul directly from the hand.
Overshooting the 'stack'
This is inevitably the player's fault for not counting, remembering, and making the utmost use of their remaining cards. In the same vein, failure to arrange cards in the most helpful order also lies on the player. One must lock the opponent out of any possibility of derailing the remaining cards from doing their job, so intercepts will be rather heavy late in the game, in particular if it's necessary to burn through an odd number of cards in deck (one, three, etc.). Psychic Bird needs a place to land, after all. CEO Amaterasu can also serve as a late game deck manipulator to finish the job.
Aaand that covers just about all the major problems one will encounter after having played the deck for an extended period of time. With some luck and the proper mindset, overcoming them is possible, so there's no need to be discouraged. If there are any further questions on how to build or play the deck, don't hesitate to ask! I've grown rather weary, so I'll have to leave the general tips, tricks, and techs plus full deck list for another post.