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 an item as a carpenter.
Clear your first instanced raid.
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.
Defeat 10,000 enemies.
Complete the main scenario.
Complete 1,000 levequests.
Complete 100 guildhests.
Successfully affix materia to an item.
Successfully affix 100 materia.
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 100 instanced raids.
Clear the Binding Coil.
Participate in PvP.
Complete 1,000 FATEs.