Here is the full list of all 31 Oafmatch achievements.
Slay Milo Randall the Sorcerer
Get three gold stars in every battle in The Shuttered Depths
Slay Jaina Randall the Sorcerer
Triumph over the Unearth invasion of Mendra
Slay the Randall twins simultaneously, preventing either of them from ascending to Sorcererhood
Get three gold stars in every battle in Agrinji's Pit
Unlock all fifteen playable characters in the campaign
Get three gold stars in every battle in Shear Valley
Get three gold stars in every battle in The Boneyard
Learn about the history of the Old Sorcerers
Get three gold stars in every battle in Rayburn's Canyon
Kill three foes with a single attack
Get three gold stars in every battle in Mendra Crags
Get a Killer Combo
Get a Monster Combo
Get three gold stars in every battle in Mendra Bay
Get three gold stars in every battle in Mendra Coast
Match six or more gems of the same color in a single match
Get a Brutal Combo
Match five or more gems of the same color in a single match
Earn three gold stars in every campaign battle
Complete Agrinji's Dungeon
Triumph over the Unearth invasion of Mendra in Campaign Plus mode
Escape alive from the Dungeon of the Dark God!
Unlock all thirty playable characters in a roguelike game
Defeat the final boss with a full party of Strength characters
Defeat the final boss with a full party of Constitution characters
Defeat the final boss with a full party of Dexterity characters
Defeat the final boss with a full party of Intelligence characters
Defeat the final boss with a full party of Wisdom characters
Defeat the final boss with a full party of Charisma characters