What kind of painting tools does one need in order to make these fantasy art drawings?
While the specific example you found turns out to be digital art, the style it's reproducing is oil painting. (And acrylic, but acrylic arose as a way to paint in oils minus the long drying time.)
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Note that a talented artist can achieve the same effect with watercolors, too:
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... but IMO such painting is hard enough without pushing your materials to their limits.