Mode is known as "Sword Type" in the English instruction manual and 剣質 in Japanese. Literal translation is "Sword Quality".

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Equip EX 極 GREEN by pressing up 6 times, down 3 times, up 4 times on either Power or Speed. Switch to the other if you mess up to try again. Saved on continue.

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Equip KAN with Scroll XII in English, called 漢 in Japanese. Unlock in EXTRA by buying all other scrolls, including the other 11 skill scrolls. Costs 12000 Points. Overwrites Power / Speed / EX.

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tl;dr

With no scrolls, the short explanation is to use Power to do amazing damage with Jump + A, A and Forward + A long presses. Use EX instead if there is a damaging enough combo to compensate, namely one that saves time with no knockdown. Speed is a worse EX since proper strategy should never lose a round.

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POWER 力 RED

• Strong attacks deal about double the damage compared to Speed. Weak attacks, such as most combo hits, deal the same.
• Different and generally worse combos than Speed.
• Have Hidden Secret Slash move for each character. Known as Super Desperation in The Last Blade 2.
• No Enigma Frenzy moves. Also called Fandango in The Last Blade 2.
• Dash + B is an unblockable charge up attack. Vulnerable while charging.
• Deal chip damage on block with all moves. Note that chip damage cannot KO.

Called "Strength" in the English instruction manual. Can also be translated as "Power".

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SPEED 技 BLUE

• Strong attacks deal about half the damage compared to Power. Weak attacks, such as most combo hits, deal the same.
• Different and generally better combos than Power.
• No Super Secret Slash moves. Known as Super Desperation in The Last Blade 2.
• Have Enigma Frenzy moves started with Down, Down + A + B. Also called Fandango in The Last Blade 2.
• Dash + B is a launching overhead, meaning it hits a crouched opponent even if blocking. Can block standing.
• Deal chip damage on block only with special moves, not normal moves. Note that chip damage cannot KO.

Called "Skill" in the English instruction manual and The Last Blade 2 trailer at 0:40, despite being labeled as "Speed" in the video. Can also be translated as "Technique".

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EX 極 GREEN

Hybrid of Speed and Power:

• Deal slightly more damage than Speed for most* attacks
• Have Speed's combos and Dash + B move.
• Have Power's Hidden Secret Slash and Speed's Enigma Frenzy moves.
• Deal chip damage on block with all moves like Power.
• Take 15% more damage from strong attacks, less penalty on weaker attacks.

*Training mode confirms that attacks dealing 7 to 13 points/pixels of damage in Speed will deal 1 point/pixel more in EX. Attacks dealing 14+ in Speed will deal 2 more. The boost applies to individual hits in every combo, though most are under 7. For context, each life bar is 64 pixels before applying damage modifiers outside of Training.

Should likely always use EX instead of Speed, given the weak AI. Notably the damage penalty is 30% in The Last Blade 2. Called "Extreme" in that game's English trailer at 0:40 and is the literal translation.

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KAN 漢 BLACK/GOLD

Turn GOLDEN! Disables blocking but can still Repel. Do not flinch from getting hit by individual attacks other than knockdown moves. First hit of combo will not flinch you but later hits will. This mode is extremely useful for speedrunning.

Modification of Power. Seems to have a slight defense advantage over Power. Appears in the Switch release trailer at 0:55. Literal translation is "Manly Man".