Here is the full list of all 18 FU'UN SUPER COMBO trophies - there are 16 bronze and 2 silver.
Kizuna Encounter: Super Tag Battle: Reach and win a bonus match after defeating Jyazu.
Kizuna Encounter: Super Tag Battle: Defeat Jyazu.
Kizuna Encounter: Super Tag Battle: Win a round without tagging out or taking damage (cannot be unlocked in VS mode).
Kizuna Encounter: Super Tag Battle: Get disarmed, then win the round without picking your weapon back up (cannot be unlocked in VS mode).
Kizuna Encounter: Super Tag Battle: Sway past an opponent 3 times in a row (cannot be unlocked in VS mode).
Kizuna Encounter: Super Tag Battle: Defeat an opponent with a Surprise Attack (cannot be unlocked in VS mode).
Kizuna Encounter: Super Tag Battle: Score a 10-hit combo or greater without using a desperation move (cannot be unlocked in VS mode).
Kizuna Encounter: Super Tag Battle: Defeat Jyazu with King Leo.
Kizuna Encounter: Super Tag Battle: Earn more than 55,000 points in the first match.
Kizuna Encounter: Super Tag Battle: Defeat an opponent within 10 counts (cannot be unlocked in VS mode).
Savage Reign: KO an opponent who's on a different plane than you are (cannot be unlocked in VS mode).
Savage Reign: Defeat King Lion.
Savage Reign: Defeat King Leo and clear the game.
Savage Reign: Win a match with a desperation move (cannot be unlocked in VS mode).
Savage Reign: Get a perfect score on both bonus stages in a single run through Arcade mode.
Savage Reign: Perform a Throw Reverse (cannot be unlocked in VS mode).
Savage Reign: Dodge an opponent's desperation move by moving to the stage's other plane (cannot be unlocked in VS mode).
Savage Reign: Score 9,000 points or more in a single round (cannot be unlocked in VS mode).