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