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