Here is the full list of all 41 Wizards Tourney achievements.
Win a Ray Fray round without being hit by the light rays
Finish a tourney.
Win a tourney playing as Ruanuku
Play a Mad Lab round
Win a Mad Lab round without anyone else scoring
Play a Totem Temple round
Play a Dragon Eggplosion round
Play an Ice Slide round
Play a Pumpkin King round
Play a Ray Fray round
Win a Pot a Potion round being a sheep
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 50 Dragon Eggplosion rounds
Play 200 Dragon Eggplosion rounds
Play 50 Mad Lab rounds
Play 200 Mad Lab rounds
Play 50 Ray Fray rounds
Play 200 Ray Fray rounds
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 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 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.