Here is the full list of all 48 Path of Exile trophies - there are 34 bronze, 11 silver, 2 gold and 1 platinum.
Have a Skill Gem reach level 20.
Defeat The Elder.
Kill Izaro and have him drop 3 treasure keys.
Complete a map that is affected by 10 or more mods.
Corrupt a map to have eight mods.
Have a Voidstone socketed in your Atlas.
Reach level 80.
Corrupt an item to have a new implicit mod.
Corrupt an Essence monster with a Remnant of Corruption.
Tag every waypoint as one character.
Fully clear an end-game Map area.
Complete Part 2.
Complete every side-quest as one character.
Kill the Depraved Trinity.
Obtain every god power.
Kill Lunaris and Solaris.
Hand in a Full Set of Divination Cards to Tasuni.
Kill Arakaali, Spinner of Shadows.
Choose an Ascendancy class.
Complete the Labyrinth.
Have at least 75% resistance to Fire, Cold, and Lightning.
Kill T'soagoth, the Brine King.
Complete Part 1.
Equip a Unique Jewel with a radius.
Kill Malachai, The Nightmare.
Use an orb to change the mods of a Strongbox.
Kill High Templar Dominus.
Freed the Scion.
Have 60 Minions at the same time.
Equip a Rare or Unique item in every non-Flask slot.
Allocate a Keystone Passive Skill.
Vanquish the Vaal Oversoul.
Equip a Unique item.
Kill Merveil, the Siren.
Obtained every trophy.
Reach level 90.
Discover all environmental lore as one character.
Create an item with six linked sockets using an Orb of Fusing.
Kill Argus.
Complete the Eternal Labyrinth.
Have two Voidstones socketed in your Atlas.
Have three Voidstones socketed in your Atlas.
Complete every map on the Atlas.
Kill Beidat, Archangel of Death.
Kill Atziri in the Apex of Sacrifice.
Kill Atziri in the Alluring Abyss.
Kill every Breachlord.
Kill the Shaper.