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.
Find an uncommon citrine gem.
Find a pezzottaite gem.
Find a ruby gem.
Let the baby dragons sleep.
Mark each living egg.
Find a chrysoprase gem.
Find a copper tourmaline gem.
Find an amethyst gem.
Mine one trillion gold.
Unlock the elementals.
Reach prestige level 10.
Reach prestige level nine.
Unlock the alchemists.
Reach prestige level eight.
Reach prestige level seven.
Mine one billion gold.
Reach prestige level six.
Reach prestige level five.
Reach prestige level four.
Reach prestige level three.
Unlock the halflings.
Reach prestige level two.
Unlock the drow.
Reach prestige level one.
Unlock the dwarves.
Mine one million gold.
Unlock the gnomes.
Unlock the goblins.
Unlock the cobolds.
Mine one thousand gold.
Unlock the peons.