Here is the full list of all 31 Realm of the Mad God achievements.
More than 100 party member level ups with a single character
More than 1000 quests completed with a single character
Completed over 65 Class Quests
Completed every dungeon type with a single character
Completed over 52 Class Quests
Dealt Killing blow to Oryx
Completed over 39 Class Quests
Completed over 26 Class Quests
More than 4 million tiles uncovered with a single character
Unlocked Mystic Class
Unlocked Sorcerer Class
Achieved fame of 1000 or more
Defeated more than 1000 gods with a single character
Achieved fame of 500
Completed over 13 Class Quests
Unlocked Trickster Class
More than 1 million tiles uncovered with a single character
Unlocked Assassin Class
Unlocked Huntress Class
Defeated more than 100 gods with a single character
Unlocked Paladin Class
Unlocked Necromancer Class
Unlocked Knight Class
Reached Level 20
Unlocked Warrior Class
Reached Level 10
Unlocked Rogue Class
Unlocked Archer Class
Unlocked Priest Class
First in a long line of heroes
More than 1000 party member level ups with a single character