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(Note: The following is based on the trial version of the game. It is currently in development and may not reflect the gameplay that resides in the final version.)
Scoring Point Items
Try to collect point items at the maximum value as much as possible. Make good use of the collection line. When this isn't possible, you could bomb and fly up to the top, although you might want to save them for a successful clear instead if you're not confident. Marisa is a bit cumbersome with this technique - if you stay at the bottom, her speed decreases and it becomes difficult to get everything. If you stay at the top, however, it becomes more difficult to destroy enemies that drop point items.
Increasing your max point value is done by gathering blue spirits and grazing. The spirit items do not move towards you above the PoC, so try to collect as many as possible, before they disappear. Try to stay as close to the boss as possible to generate them quickly, giving a good fill at your trance gauge. Grazing, on the other hand, may be a better choice if this becomes impossible, although it doesn't generate Trance. Bosses are also a good chance to boost point item value and score a huge burst by using Trance and standing right in front of them.
Practice is of utmost importance. It becomes a lot easier to understand where every bullet and enemy spawns on each stage by playing often. Watch your friends' replays or see how the top hardcore players rake in the masses and get a feeling of how you can incorporate it into your gameplay.
When it gets too rough, try on a lower difficulty and work your way up to the top. And don't forget to have fun.
Bosses and Spirits
Divine spirits will scatter around the bosses as you damage them. If you are sufficiently close to them, you will be able to collect them before they scatter at all; if you are almost in point blank range, the speed of divine spirits coming out increases dramatically. There are several attacks where it is completely safe to stand in front of the boss at some points (such as Yuyuko's second card or Kyouko's midboss card), so it would be wise to do so during these moments while unfocused. Just remember to dodge when the bullets come along.
Using Your Trance Wisely
During Trance mode, the effect of divine spirits increase dramatically - blue spirits now give +100 to maximum point item values, and red/green spirits give +2 to your life and bomb gauge, respectively. Thus, it is important to memorize select points where you can enter Trance to ensure maximum profit from divine spirits. This is especially important if your goal is to obtain a lot of lives and bombs from Trance, as only a few enemies on stages will drop red and green spirits, and wise use of Trance can make a very large difference in the amount of extends you obtain.
Reimu is, as usual, arguably the most flexible character for beginners. Her shot types are very similar to their use in Imperishable Night; normal shot is homing seals (though they "home" in on enemies with somewhat less accuracy, somewhere between "traditional" ReimuA and UFO's ReimuB), focused shot is more powerful and faster straight ahead. Her smaller hitbox can allow less experienced players to manoeuver more easily. Ultimately this is the Reimu that we all know and love.
Marisa's shots are all about enemy sweeping, but her high speed can make her difficult to control. Unfocused, her shot is a set of lasers (however they have been gimped somewhat, as they no longer pierce enemies); focused, a set of slow-moving missiles that have a slight splash damage effect. At levels 3 and 4, two of her lasers shoot slightly outward diagonally, making her somewhat more effective at sweeping enemies; unfortunately, this means sacrificing some power straightforward when dealing with bosses. The option spread also now makes it mostly impossible to hit bosses with all four by getting in close proximity.
Marisa becomes exceptionally deadly during Trance, so use that to your advantage.
Sanae's shot type is significantly different from that of her previous appearance in UFO. She arguably deals the least damage of the four, but her wide spread shot types can be helpful for beginners. Unfocused, she shoots green wind slashes in a multi-directional forward spread; focused, direct forward waves of the same bullets. Due to the nature of her focused shot it can be tricky to find a spot in which all of her bullets hit the enemy, but there is always a decent chance that at least some of her shots will be making contact at any given time. Her special ability allows her to reach Trance more often, which can also be beneficial to players whose dodging skills are subpar but are good at survival-bombing. Unfortunately, all of this makes her less flexible in the hands of high-level players.
Youmu can definitely pack a punch. Unfocused, she fires countless TINY CUTS: two streams from her directly, and one more from each option, leading to a maximum of 6 streams of bullets. Her focused shot is rather unique in that it is a charged attack: hold down focus and attack for a moment and then release (there is an audio cue for when the attack is charged) and she creates a barrage of very large, very powerful horizontal sword swipes which annihilates most regular enemies on contact, including larger fairies. It also does rather decent damage to bosses, though at higher levels the regular focused shot can probably inflict more damage more safely. Her options trail behind her in a queue, so if you want to spread fire horizontally, move left or right, and if you want to focus fire forward, move up or down (so the options stand on top of each other). Unfortunately, this means that it can be difficult to significantly damage bosses without being aligned with them or close to them vertically.
Her Trance shot is a "constant" version of her focus shot, which can make it great for taking care of large swarms of enemies coming in from both sides of the screen at once.