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