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