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