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