Here is the full list of all 34 Goldmine achievements.
Find an incredibly rare alaricium gem.
Find a rare chrysoberyl gem.
Mine one quadrillion gold.
Mark each living egg.
Let the baby dragons sleep.
Find an uncommon citrine gem.
Find a ruby gem.
Find a pezzottaite gem.
Unlock the elementals.
Mine one trillion gold.
Find an amethyst gem.
Find a copper tourmaline gem.
Find a chrysoprase gem.
Unlock the alchemists.
Reach prestige level 10.
Reach prestige level nine.
Reach prestige level eight.
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.