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