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