Here is the full list of all 34 Goldmine achievements.
Find a rare chrysoberyl gem.
Find a ruby gem.
Let the baby dragons sleep.
Mark each living egg.
Find a pezzottaite gem.
Unlock the elementals.
Mine one trillion gold.
Find a copper tourmaline gem.
Find an amethyst gem.
Find a chrysoprase gem.
Reach prestige level 10.
Reach prestige level nine.
Reach prestige level eight.
Unlock the alchemists.
Reach prestige level seven.
Mine one billion gold.
Unlock the halflings.
Reach prestige level six.
Reach prestige level five.
Reach prestige level four.
Reach prestige level three.
Unlock the drow.
Reach prestige level two.
Unlock the dwarves.
Reach prestige level one.
Mine one million gold.
Unlock the gnomes.
Unlock the goblins.
Unlock the cobolds.
Mine one thousand gold.
Unlock the peons.
Mine one quadrillion gold.
Find an uncommon citrine gem.
Find an incredibly rare alaricium gem.