Here is the full list of all 34 Goldmine achievements.
Find an uncommon citrine gem.
Mine one quadrillion gold.
Mark each living egg.
Find a rare chrysoberyl gem.
Find an incredibly rare alaricium gem.
Find a ruby gem.
Let the baby dragons sleep.
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.
Reach prestige level eight.
Reach prestige level seven.
Unlock the alchemists.
Unlock the halflings.
Mine one billion gold.
Reach prestige level six.
Unlock the drow.
Reach prestige level five.
Reach prestige level four.
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.