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