From Touhou Wiki:
Mystical Chain is a fighter game set in Gensokyo. Every stage has five levels. The first four levels of any stage feature a growing number of small opponents that need to be defeated for the level to clear. The final level is a boss fight, featuring two characters with many spellcards that need to be defeated before moving on.
There are three main characters: Marisa Kirisame, Patchouli Knowledge, and Alice Margatroid. You may choose any two of them. The two characters have to work together to defeat enemies that could be difficult to defeat alone. Ways of using the two characters effectively will be discussed in the strategy section below.
There are four levels of difficulty: Easy, Normal, Hard and Lunatic. The harder difficulties' opponents do more damage, and their attacks feature more danmaku. Additionally, the harder difficulties have fewer magic charges, which are used to activate special attacks. On Hard and Lunatic, enemies that are knocked down have increasingly long invincible frames as they get up, and bosses recover much quicker from being knocked out of spellcards. On Lunatic, even common enemies have the chance to attack you twice before their invincibility wears off. If you get to a certain stage with a specific team, you can later jump to it on the difficulty screen provided you got a proper game over.
As you advance through the stages, you are awarded additional magic charges. Otherwise there is no difference between your characters in the advanced levels.
Characters share magic charges as well as a single spellcard gauge. When one character uses a strong attack, or when switching between characters, the other character has one less magic charge to work with. However, they regenerate when not in use rather quickly.
Spell cards use a spellcard gauge to fire. Under the player's health bar is his spellcard gauge. It is divided into three sections. When casting a spell card, one section (one third of the total bar) is consumed. The spellcard gauge regenerates over time, and is recovered more quickly as the player dishes out damage.
Controls:
Arrow keys: Movement and aiming
Z: Attack
X: Jump
A: Spellcard
C: Switch master and slave
Space: Pause the game and pop up the menu
F5: Pause, can resume with F5
F1: Go back to main menu, progress is not saved.
Screen Layout
A - Master character's health bar. The slave character's health bar is behind it.
B - Boss health bar.
C - Spellcard gauge.
D - Chaining indicator (appears when landing hits)
E - Boss spellcard remaining indicator.
F - Master character. Note the orange spell circle.
G - Slave character in ambush mode. Note the blue spell circle.
H - Gems, which are released after the completion of a spellcard, kills, or certain attacks.
I - Magic charges.
J - An understandably happy phoenix.
K - NEET.