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