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