Here is the full list of all 46 Diablo III trophies - there are 37 bronze, 5 silver, 3 gold and 1 platinum.
Buy each type of item from merchants.
Kill Diablo in Nightmare mode.
Buy all stash upgrades.
Equip all Inventory slots with items that have a minimum required level of 25 or higher.
Fully equip one of your followers.
Recruit the Templar, Scoundrel, and Enchantress.
Complete all quests in Act IV.
Kill Diablo in Normal mode.
Complete all quests in Act III.
Kill Azmodan in Normal mode.
Reach level 30.
Complete all quests in Act II.
Kill 500 elite (champion, rare, or unique) enemies.
Kill Belial in Normal mode.
Craft 5 items.
Combine gems.
Kill Maghda in Normal mode.
Complete all quests in Act I.
Kill the Butcher in Normal mode.
Kill one of the unique enemies listed in the Never Seen That Before Challenge.
Use a merchant to repair an item.
Reach level 10.
Equip a rare (yellow) item.
Kill the Skeleton King in Normal mode.
Equip a legendary (orange) item.
Collected all other Diablo III Trophies.
Reach level 60.
Reach level 30 in Hardcore mode.
Kill the Skeleton King in Inferno mode.
Kill the Butcher in Inferno mode.
Kill Maghda in Inferno mode.
Kill Belial in Inferno mode.
Kill Azmodan in Inferno mode.
Kill Diablo in Hell mode.
Kill Diablo in Inferno mode.
Complete all the Butcher triumph challenges.
Complete all the Belial triumph challenges.
Complete all the Azmodan triumph challenges.
Complete all the Diablo triumph challenges.
Equip all Inventory slots with items that have a minimum required level of 60 or higher.
Complete all the main character, follower, and artisan conversation challenges.
Raise the Blacksmith to level 10.
Raise the Jeweler to level 10.
Pick up 500,000 gold.
Pick up 5,000,000 gold.
Kill 100 Treasure Goblins.