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