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.
Let the baby dragons sleep.
Mark each living egg.
Find a ruby gem.
Mine one trillion gold.
Find an amethyst gem.
Find a pezzottaite gem.
Unlock the elementals.
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.
Mine one billion gold.
Unlock the halflings.
Reach prestige level six.
Reach prestige level five.
Reach prestige level four.
Unlock the drow.
Reach prestige level three.
Unlock the dwarves.
Reach prestige level two.
Reach prestige level one.
Unlock the gnomes.
Mine one million gold.
Unlock the goblins.
Unlock the cobolds.
Mine one thousand gold.
Unlock the peons.