A few hours into the game in the main story questline you will enter a town called Parum. Report to the tamer guild and you will receive a bronze badge. You need this before people will let you craft cores so go to the main office first. Once you have that head left past a bridge and you should see a dragon statue in a courtyard. Enter the main building and head back to meet Bonnie. She let's you craft cores in exchange for element shards.