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.
Mark each living egg.
Let the baby dragons sleep.
Unlock the elementals.
Find a ruby gem.
Find a rare chrysoberyl gem.
Mine one trillion gold.
Find a copper tourmaline gem.
Find a pezzottaite gem.
Find a chrysoprase gem.
Find an amethyst gem.
Reach prestige level 10.
Unlock the alchemists.
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.
Unlock the drow.
Reach prestige level four.
Reach prestige level three.
Reach prestige level two.
Unlock the dwarves.
Reach prestige level one.
Unlock the gnomes.
Mine one million gold.
Unlock the goblins.
Unlock the cobolds.
Mine one thousand gold.
Unlock the peons.