Here is the full list of all 18 7776 II: Dwarven Greed achievements.
Win without a single coal.
Win as King.
Win as Mechanic.
Win as Student.
Win without using special ability.
Select a combination after using ability.
Win 100 games.
Get 4 coals in a game.
Get a diamond, a sapphire, an emerald, a coal and some beer.
Play draw.
Select the same combination as opponent. Six times.
Win three games in a row.
Get two diamonds in a game.
Have a poker.
Lose without a single coal.
Have a straight.
Both players didn't get a straight.
Don't pay attention to poker.