Here is the full list of all 38 Minion Masters achievements. It takes around 200 hours to unlock all of the achievements on Windows.
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Reach the Bronze League
Win 10 Ranked Battles
Win against 8 different Masters
Complete 3 Daily Quests
Complete 5 Achievements
Reach the Stone League
Acquire a collection of 50 cards
Craft a Common card
Complete 5 solo challenges
Win 3 Ranked Battles
Complete 15 Achievements
Complete 30 Achievements
Play a friendly challenge with 3 different friends.
Reach the Silver League
Use 20 Resource Tokens
Use 50 Resource Tokens
Use 100 Resource Tokens
Use 25 Power Tokens
Use 100 Power Tokens
Use 250 Power Tokens
Win a Ranked Battle with less than 100 Health left
Craft a Rare card
Craft a Supreme card
Craft a Legendary card
Win 50 Ranked Battles
Win 100 Ranked Battles
Win 500 Ranked Battles
Win a Ranked battle with 8 different Masters
Acquire a collection of 100 cards
Acquire a collection of 150 cards
Complete 10 solo challenges
Create 3 decks
Complete 10 Daily Quests
Complete 25 Daily Quests
Complete 50 Daily Quests
Complete 100 Daily Quests
Play 5 spells in a row during a Ranked Match and then win