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.
Mark each living egg.
Let the baby dragons sleep.
Find a ruby gem.
Find a pezzottaite gem.
Find an amethyst gem.
Find a chrysoprase gem.
Find a copper tourmaline 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.
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.
Mine one million gold.
Unlock the gnomes.
Unlock the goblins.
Unlock the cobolds.
Mine one thousand gold.
Unlock the peons.