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