Here is the full list of all 43 Diablo III: Reaper of Souls - there are Ultimate Evil Edition achievements worth 1,000 gamerscore.
Use a merchant to repair an item.
Socket a gem in an item.
Kill the Skeleton King.
Kill the Butcher.
Complete all quests in Act I.
Kill Maghda.
Craft 5 items.
Craft 100 items.
Combine gems.
Pick up 500,000 gold.
Recruit the Templar, Scoundrel, and Enchantress.
Equip all Inventory slots with Legendary items that have a minimum required level of 70 or higher.
Complete 5 Bounties.
Kill 500 Monsters while in Nephalem Rifts.
Finish a Nephalem Rift within 15 Minutes.
Kill Zoltun Kulle.
Kill Belial.
Complete all quests in Act II.
Kill Ghom.
Kill the Siegebreaker Assault Beast.
Kill Azmodan.
Complete all quests in Act III.
Kill Diablo.
Complete all quests in Act IV.
Kill Urzael.
Kill Adria.
Kill Malthael.
Complete all quests in Act V.
Reach level 70.
Kill 500 elite (champion, rare, or unique) enemies.
Raise the Blacksmith to level 12.
Raise the Jeweler to level 12.
Raise the Mystic to level 12.
Replace a property with Enchanting.
Acquire the Mystic.
Complete 500 Bounties.
Reach level 70 in Hardcore mode.
Kill Diablo in Hardcore mode.
Kill Malthael in Hardcore mode.
Reach level 70 with 6 different classes.
Kill 100 Treasure Goblins.
Get a destruction callout for breaking 50 objects.
Enchant all your equipment slots.