Here is the full list of all 21 Rift Wizard achievements.
Complete the Vampire Hunter Trial
Win One Game
Reach Level Twenty
Reach Level Ten
Win Five Games
Win Two Consecutive Games
Win Three Consecutive Games
Win Five Consecutive Games
Win Ten Games
Complete the Danger Brigade Trial
Complete the Flamefest Trial
Complete the Giantslayer Trial
Complete the Humble Horde Trial
Complete the Improviser Trial
Complete the Menagerie Trial
Complete the Sorcerer Ascetic Trial
Complete the Wizard Warlords Trial
Complete the Thrify Wizard Trial
Complete the Trollpath Trial
Complete the Wolfer Trial
Complete the Limited Spellbook Trial