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