A Digicore is the base of any digimon. To gain Digicores you will have to scan Mercenary Digi-eggs, however you don't always get Digicores as you can get datas. Also you can get 1 to 12 Digicores when you scan Mysterious Magic Eggs or Mysterious Top Quality Eggs. Those items are dropped by any Card Boss. And Monster Cards Lv5 monsters can drop between 1 and 3 Digicores each.
Digicores can also be sold for Mercenary Digi-eggs or Clones (B/C/D) within the DATS Center at the Kamemon Core Shop.