RNA viruses are notorious for their ability to evolve rapidly under novel environments. It is known that the high mutation rate of RNA viruses can generate huge genetic diversity to facilitate viral adaptation. However, less attention has been paid to the underlying fitness landscape that represents the selection forces on viral genomes. Here we systematically quantified the distribution of fitness effects (DFE) of single amino acid substitutions (86 amino acids total) in the drug-targeted region of NS5A protein of Hepatitis C Virus (HCV). We found that the majority of non-synonymous substitutions incur large fitness costs, suggesting that NS5A protein is highly optimized in natural conditions. Furthermore, we characterized the evolutionary potential of HCV by subjecting the mutant viruses to varying concentrations of an NS5A inhibitor Daclatasvir. As the selection pressure increases, the DFE of beneficial mutations shifts from an exponential distribution to a heavy-tailed distribution with a disproportionate number of exceptionally fit mutants. The number of available beneficial mutations and the selection coefficient are both found to increase at higher levels of antiviral drug concentration, as predicted by a pharmacodynamics model describing viral fitness as a function of drug concentration. Our large-scale fitness data of mutant viruses also provide insights into the biophysical basis of evolutionary constraints and the role of the genetic code in protein evolution.