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