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