Here is the full list of all 35 Quest of Wizard achievements.
Open all the chests in Level 1
Open all the chests in Level 2
Open all the chests in Level 3
Open all the chests in Level 4
Complete all levels and defeat the boss in the Goblin Forest
Defeat the boss in Goblin Forest without damage
Open all the chests in Level 6
Open all the chests in Level 7
Open all the chests in Level 8
Open all the chests in Level 9
Complete all levels and defeat the boss in the Troll Desert
Defeat the boss in Troll Desert without damage
Open all the chests in Level 11
Open all the chests in Level 12
Open all the chests in Level 13
Open all the chests in Level 14
Complete all levels and defeat the boss in the Graveyard
Defeat the boss in Graveyard without damage
Open all the chests in Level 16
Open all the chests in Level 17
Open all the chests in Level 18
Open all the chests in Level 19
Complete all levels and defeat the boss in the Snowy Mountains
Defeat the boss in Snowy Mountains without damage
Open all the chests in Level 21
Open all the chests in Level 22
Open all the chests in Level 23
Open all the chests in Level 24
Complete all levels and defeat the boss in the Demon Wasteland
Defeat the boss in Demon Wasteland without damage
Complete all game
Upgrade All Main Spells
Buy All Additional Spells
Buy All Upgrades
Buy All Items