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