Here is the full list of all 43 Fantasy Strike trophies - there are 22 bronze, 18 silver, 2 gold and 1 platinum.
Win a game with a successful Yomi Counter.
Win a round with a successful Yomi Counter.
Complete Arcade mode with any character.
Win 5 matches against CPU opponents.
Complete 5 Standard matches in Local Play.
Play as Rook 10 times in online modes.
Play as Midori 10 times in online modes.
Destroy 5 projectiles with Thunderclap as Rook.
Play 10 Ranked Matches.
Watch a Friend battle in Spectator Mode.
Win two consecutive rounds while in Dragon Form the entire time as Midori.
Play as Valerie 10 times in online modes.
Play as Argagarg 10 times in online modes.
Normal throw an opponent 3 times in one round without them Yomi Countering, for some reason.
Play as Grave 10 times in online modes.
Stack poison 3 times as Argagarg.
Summon a Mini-Rook as Lum.
Play as Lum 10 times in online modes.
Play as Geiger 10 times in online modes.
Complete 10 matches in Local Play.
Play as Setsuki 10 times in online modes.
Win a round with Dragonheart while at 1 health remaining as Jaina.
Play as DeGrey 10 times in online modes.
Play as Jaina 10 times in online modes.
Challenge a Friend to a Friendly Match.
Perform a 5+ damage combo in Practice mode.
Spend 5 minutes in Practice Mode.
Activate the Frame Step feature in Practice mode.
Win 5 Ranked Matches.
Complete 5 Team Battle matches in Local Play.
Win your first Ranked Match.
Win a match against a CPU opponent.
Dominate your opponent's wimpy projectile with your powerful one as Grave.
Complete the tutorial.
Collect all trophies.
Beat at least 7 opponents in Daily Challenge.
Complete Survival: 20 Opponents.
Complete Survival: 35 Opponents.
Complete Survival: 50 Opponents.
Complete Survival: 10 Cruel Opponents.
Reach Silver League in Ranked Mode.
Perform a 5 damage combo as Setsuki.
Counter-hit the opponent into a 4 damage combo with DeGrey.