Here is the full list of all 41 Wizards Tourney achievements.
Play a Totem Temple round
Play an Ice Slide round
Play a Pumpkin King round
Play a Pot a Potion round
Play 50 Pot a Potion rounds
Play 200 Pot a Potion rounds
Play 50 Pumpkin King rounds
Play 200 Pumpkin King rounds
Play 50 Ice Slide rounds
Play 200 Ice Slide rounds
Play a Dragon Eggplosion round
Play 50 Dragon Eggplosion rounds
Play 200 Dragon Eggplosion rounds
Play a Mad Lab round
Play 50 Mad Lab rounds
Play 200 Mad Lab rounds
Play a Ray Fray round
Play 50 Ray Fray rounds
Play 200 Ray Fray rounds
Win a Pot a Potion round being a sheep
Win a Pumpkin King round without touching the Rotten Pumpkin
Win an Ice Slide round with four or less platforms remaining
Win a Dragon Eggplosion round without being hit by the dragon's fireballs
Win a Mad Lab round without anyone else scoring
Win a Ray Fray round without being hit by the light rays
Win a tourney playing as Magus
Win a tourney playing as Wushi
Win a tourney playing as Meiga
Win a tourney playing as Achichín
Win a tourney playing as Draoidh
Win a tourney playing as Shama
Win a tourney playing as Varth-Lokkur
Win a tourney playing as Ruanuku
Win a tourney playing as Wakhan
Win a tourney playing as Nauali
Win a tourney playing as Hukri
Win a tourney playing as Sahir
Play 50 Totem Temple rounds
Play 200 Totem Temple rounds
Win a Totem Temple round by only building towers of your color.
Finish a tourney.