Here is the full list of all 39 Final Fantasy XIV: A Realm Reborn trophies - there are 20 bronze, 15 silver, 3 gold and 1 platinum.
Complete 1,000 FATEs.
Join a FATE.
Clear 100 instanced raids.
Clear your first instanced raid.
Complete the main scenario.
Complete your first quest.
Complete your first guildhest.
Defeat 10,000 enemies.
Defeat your first enemy.
Obtain all available FINAL FANTASY XIV: A Realm Reborn trophies.
Complete your first levequest.
Complete 1,000 levequests.
Complete 100 guildhests.
Successfully affix materia to an item.
Successfully affix 100 materia.
Synthesize an item as a carpenter.
Synthesize 1,000 items as a carpenter.
Synthesize an item as a blacksmith.
Synthesize 1,000 items as a blacksmith.
Synthesize an item as an armorer.
Synthesize 1,000 items as an armorer.
Synthesize an item as a goldsmith.
Synthesize 1,000 items as a goldsmith.
Synthesize an item as a leatherworker.
Synthesize 1,000 items as a leatherworker.
Synthesize an item as a weaver.
Synthesize 1,000 items as a weaver.
Synthesize an item as an alchemist.
Synthesize 1,000 items as an alchemist.
Synthesize an item as a culinarian.
Synthesize 1,000 items as a culinarian.
Mine a mineral deposit.
Mine 1,000 mineral deposits.
Log at a mature tree.
Log at 1,000 mature trees.
Fish with your own rod and bait.
Fish 1,000 times.
Clear the Binding Coil.
Participate in PvP.