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