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