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.
Synthesize 1,000 items as a leatherworker.
Complete 1,000 FATEs.
Clear the Binding Coil.
Complete 100 guildhests.
Defeat 10,000 enemies.
Log at 1,000 mature trees.
Mine 1,000 mineral deposits.
Clear 100 instanced raids.
Complete the main scenario.
Successfully affix materia to an item.
Participate in PvP.
Clear your first instanced raid.
Mine a mineral deposit.
Synthesize an item as an alchemist.
Synthesize an item as a weaver.
Synthesize an item as a goldsmith.
Log at a mature tree.
Synthesize an item as a leatherworker.
Synthesize an item as a carpenter.
Fish with your own rod and bait.
Synthesize an item as a blacksmith.
Synthesize an item as an armorer.
Synthesize an item as a culinarian.
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.
Complete 1,000 levequests.
Successfully affix 100 materia.
Synthesize 1,000 items as a carpenter.
Synthesize 1,000 items as a blacksmith.
Synthesize 1,000 items as an armorer.
Synthesize 1,000 items as a goldsmith.
Synthesize 1,000 items as a weaver.
Synthesize 1,000 items as an alchemist.
Synthesize 1,000 items as a culinarian.
Fish 1,000 times.