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