Here is the full list of all 34 Goldmine achievements.
Find an incredibly rare alaricium gem.
Find a rare chrysoberyl gem.
Mark each living egg.
Let the baby dragons sleep.
Mine one quadrillion gold.
Find an uncommon citrine gem.
Find a ruby gem.
Find a pezzottaite gem.
Unlock the elementals.
Mine one trillion gold.
Find a chrysoprase gem.
Find a copper tourmaline gem.
Find an amethyst gem.
Reach prestige level 10.
Reach prestige level nine.
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.
Reach prestige level one.
Unlock the alchemists.
Mine one billion gold.
Unlock the halflings.
Unlock the drow.
Unlock the dwarves.
Mine one million gold.
Unlock the gnomes.
Unlock the goblins.
Unlock the cobolds.
Mine one thousand gold.
Unlock the peons.