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.
Clear your first instanced raid.
Log at a mature tree.
Synthesize an item as a leatherworker.
Synthesize an item as a carpenter.
Synthesize an item as a weaver.
Synthesize an item as a goldsmith.
Synthesize an item as a blacksmith.
Synthesize an item as an armorer.
Complete your first levequest.
Fish with your own rod and bait.
Synthesize an item as a culinarian.
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 your first guildhest.
Complete 100 guildhests.
Successfully affix materia to an item.
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 an item as an alchemist.
Synthesize 1,000 items as an alchemist.
Synthesize 1,000 items as a culinarian.
Mine a mineral deposit.
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.