Vamp had quite a bit an out of the ordinary story.
So Vamp got his training in the Navy SEALs anti-terrorist squad Dead Cell for which he was a member. So basically about this skills with knives, guns, etc. that's all we know so far.
For his "supernatural" abilities well:
Prior to his membership of the Navy SEALs anti-terrorist squad Dead
Cell, Vamp was subjected to experimental nanomachines, which would
allow him to heal from wounds and sickness at an unusually accelerated
rate. The nanomachines had previously been developed by Dr. Naomi
Hunter, and her design was later perfected by other interested
parties. The experiment proved to be a success, resulting in Vamp
gaining his apparent immortality. At some point later, Vamp joined
Dead Cell, and was one of the first members to join the unit during
For additional information on Vamp you can check Vamps Wiki Page!