Here is the full list of all 49 Metal Slug Tactics trophies - there are 34 bronze, 12 silver, 2 gold and 1 platinum.
Unlock all trophies.
Launch 3 Special Actions in 1 turn with Marco.
Deal 15 Health Points of damage in 1 attack with Marco (excluding syncs).
Win a run with Marco.
Unlock Marco's epilogue.
Kill 4 enemies in 1 Special Action with Eri.
Deal damage to 5 different enemies in 1 turn with Eri.
Win a run with Eri.
Unlock Eri's epilogue.
Unlock all the regions in the game.
Kill 3 enemies in 1 Special Action with Tarma.
Reach 8 Dodge points with Tarma.
Win a run with Tarma.
Unlock Tarma's epilogue.
Launch Nudge twice in 1 turn with Fio.
Fire Fio's weapons 3 times in a turn.
Win a run with Fio.
Unlock Fio's epilogue.
Win a run having completed 2 regions in total.
Apply Mind Control to 4 enemies in 1 turn with Trevor.
Hit 4 separate targets in 1 turn with Trevor.
Win a run with Trevor.
Unlock Trevor's epilogue.
Win a run with 6 different characters.
Deal damage to 5 different enemies in 1 turn with Nadia and her bots.
Deal 9 Health Points of damage to a single enemy in 1 turn with Electric Mines alone.
Win a run with Nadia.
Unlock Nadia's epilogue.
Win a run having completed 4 regions in total.
Deal 15 Health Points of damage in 1 special action with Ralf.
Regain 2 Action Points in 1 turn with Ralf.
Win a run with Ralf.
Unlock Ralf's epilogue.
Win a run with 8 different characters.
Have 3 Afterimages in play simultaneously.
Trigger a synchronization with 3 Afterimages participating.
Win a run with Leona.
Unlock Leona's epilogue.
Win a run having completed 3 regions in total.
Apply and trigger Fragile each turn with Clark in a mission that lasts 5 turns or more.
Deal 10 Health Points of damage on an enemy in 1 special action with Clark.
Win a run with Clark.
Unlock Clark's epilogue.
Get the true ending.
Get all the inter-team dialogs.
Meet all of Morden's generals.
Defeat Morden with Reinforcement maxed out.
Defeat all region bosses once.
Defeat Morden after first completing all regions.