Here is the full list of all 34 Goldmine achievements.
Mine one quadrillion gold.
Find an incredibly rare alaricium gem.
Find an uncommon citrine gem.
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 chrysoprase gem.
Find a copper tourmaline gem.
Find an amethyst gem.
Reach prestige level 10.
Reach prestige level nine.
Unlock the alchemists.
Reach prestige level eight.
Reach prestige level seven.
Mine one billion gold.
Unlock the halflings.
Reach prestige level six.
Reach prestige level five.
Unlock the drow.
Reach prestige level four.
Reach prestige level three.
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.